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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Use the functions in Example 4 to find Af2Bg1Ch8Df3h5 Find the domains of functions F,G,andH : Fx=x23x+1Gx=5x+3Hx=2x Repeat Example 6 for fx=x24x+9. Using Function Notation, find (A) fa (B) fa+h (C) fa+h (D) fa+hfah,h0 The financial department using statistical techniques, produced the data in Table, where Cx is the cost in millions of dollars for manufacturing and selling x million cameras. Table Cost Data Using special analytical techniques (regression analysis), an analyst produced the following cost function to model the Table 6 data: Cx=156+19.7x 1x15 …… (5) (a) Plot the data in Table 6. Then sketch a graph of equation (5) in the same coordinate system. (b) Using the revenue function from Example 7(B), what is the company’s profit function for this camera, and what is its domain? (c) Complete Table 7, computing profits to the nearest million dollars. (d) Plot the data in Table 7. Then sketch a graph of the profit function using these points. (e) Graph the profit function on a graphing calculator.In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. y=x+1 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. x=y+1 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. x=y2 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. y=x2 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. y=x3 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. x=y3 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. xy=6 In Problems 1-8, use point-by-point plotting to sketch the graph of each equation. xy=12 Indicate whether each table in Problems 9-14 specifies a function.Indicate whether each table in Problems 9-14 specifies a function.Indicate whether each table in Problems 9-14 specifies a function.Indicate whether each table in Problems 9-14 specifies a function.Indicate whether each table in Problems 9-14 specifies a function.Indicate whether each table in Problems 9-14 specifies a function.Indicate whether each graph in Problems 15-20 specifies a function.Indicate whether each graph in Problems 15-20 specifies a function.Indicate whether each graph in Problems 15-20 specifies a function.Indicate whether each graph in Problems 15-20 specifies a function.Indicate whether each graph in Problems 15-20 specifies a function.Indicate whether each graph in Problems 15-20 specifies a function.In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. y=3x+18 In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. y=4x+1x In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. y + 5x2=7 In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. 2x4y6=0 In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. x=8y+9 In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. x+xy+1=0 In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. yx2+2=10x2 In Problems 21-28, each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither. yx2+3+2x4=1 In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=1x In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=x23 In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=x21 In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=3x2 In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=4x3 In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=x32 In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=8x In Problems 29-36, use point-by-point plotting to sketch the graph of each function. fx=6x In Problems 37 and 38, the three points in the table are on the graph of the indicated function f. Do these three points provide sufficient information for you to sketch the graph of y=fx ? Add more points to the table until you are satisfied that your sketch is a good representation of the graph of y=fx for 5x5. fx=2xx2+1 In Problems 37 and 38, the three points in the table are on the graph of the indicated function f. Do these three points provide sufficient information for you to sketch the graph of y=fx ? Add more points to the table until you are satisfied that your sketch is a good representation of the graph of y=fx for 5x5. fx=3x2x2+2 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. y=f5 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. y=f4 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. y=f5 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. y=f2 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. fx=0,x0 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. fx=4 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. fx=5 In Problems 39-46, use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer. fx=0 In Problems 47-52, find the domain of each function. Fx=2x3x2+3 In Problems 47-52, find the domain of each function. Hx=72x2x4 In Problems 47-52, find the domain of each function. fx=x2x+4 In Problems 47-52,find the domain of each function. gx=x+1x2 In Problems 47-52,find the domain of each function. gx=7x In Problems 47-52, find the domain of each function. Fx=15+x In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. 2x+5y=10 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. 6x7y=21 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. yx+y=4 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. xx+y=4 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. x3+y3=27 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. x2+y2=9 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. x3y2=0 In Problems 53-60, does the equation specify a function with independent variable x ? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. xy3=0 In Problems 61-74, find and simplify the expression if fx=x24. f5x In Problems 61-74, find and simplify the expression if fx=x24. f3x In Problems 61-74, find and simplify the expression if fx=x24. fx+2 64E In Problems 61-74, find and simplify the expression if fx=x24. fx2 66E 67E In Problems 61-74, find and simplify the expression if fx=x24. fx4 In Problems 61-74, find and simplify the expression if fx=x24. f2+fh In Problems 61-74, find and simplify the expression if fx=x24. f3+fh In Problems 61-74, find and simplify the expression if fx=x24. f2+h 72E In Problems 61-74, find and simplify the expression if fx=x24. f2+hf2 74E In Problems 75-80, find and simplify each of the following, assuming h0 in C. Afx+hBfx+hfxCfx+hfxh fx=4x3 In Problems 75-80, find and simplify each of the following, assuming h0 in C. Afx+hBfx+hfxCfx+hfxh fx=3x+9 In Problems 75-80, find and simplify each of the following, assuming h0 in C. Afx+hBfx+hfxCfx+hfxh fx=4x27x+6 In Problems 75-80, find and simplify each of the following, assuming h0 in C. Afx+hBfx+hfxCfx+hfxh fx=3x2+5x8 In Problems 75-80, find and simplify each of the following, assuming h0 in C. Afx+hBfx+hfxCfx+hfxh fx=x20x In Problems 75-80, find and simplify each of the following, assuming h0 in C. Afx+hBfx+hfxCfx+hfxh fx=xx+40 Problems 81-84 refer to the area A and perimeter P of a rectangle with length l and width w (see the figure). The area of a rectangle is 25sqin. Express the perimeter Pw as a function of the width w, and state the domain of this function.Problems 81-84 refer to the area A and perimeter P of a rectangle with length l and width w (see the figure). The area of a rectangle is 81sqin. Express the perimeter Pl as a function of the length l, and state the domain of this function.Problems 81-84 refer to the area A and perimeter P of a rectangle with length l and width w (see the figure). The perimeter of a rectangle is 100m. Express the area Al as a function of the length l, and state the domain of this function.Problems 81-84 refer to the area A and perimeter P of a rectangle with length l and width w (see the figure). The perimeter of a rectangle is 160m. Express the area Aw as a function of the width w, and state the domain of this function.Price-demand. A company manufactures memory chips for microcomputers. Its marketing research department, using statistical techniques, collected the data shown in Table 8, where p is the wholesale price per chip at which x million chips can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price demand function to model the data: px=753x1x20 (a) Plot the data points in Table 8, and sketch a graph of the price-demand function in the same coordinate system. (b) What would be the estimated price per chip for a demand of 7 million chips? For a demand of 11 million chips?Price-demand. A company manufactures notebook computers. Its marketing research department, using statistical techniques, collected the data shown in Table 9, where p is the wholesale price per computer at which x thousand computers can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price-demand function to model the data: px=200060x1x25 (a) Plot the data points in Table 9, and sketch a graph of the price-demand function in the same coordinate system. (b) What would be the estimated price per computer for a demand of 11,000 computers? For a demand of 18,000 computers?Revenue. (a) Using the price-demand function px=753x1x20 from Problem 85, write the company’s revenue function and indicate its domain. (b) Complete Table 10, computing revenues to the nearest million dollars. (c) Plot the points from part B and sketch a graph of the revenue function using these points. Choose millions for the units on the horizontal and vertical axes.Revenue. (a) Using the price-demand function px=200060x1x25 from Problem 86, write the company’s revenue function and indicate its domain. (b) Complete Table 11, computing revenues to the nearest thousand dollars. (c) Plot the points from part (B) and sketch a graph of the revenue function using these points. Choose thousands for the units on the horizontal and vertical axes.Profit. The financial department for the company in Problems 85 and 87 established the following cost function for producing and selling x million memory chips: Cx=125+16x million dollars (a) Write a profit function for producing and selling x million memory chips and indicate its domain. (b) Complete Table 12, computing profits to the nearest million dollars. (c) Plot the points in part (B) and sketch a graph of the profit function using these points.Profit. The financial department for the company in Problems 86 and 88 established the following cost function for producing and selling x thousand notebook computers: Cx=4,000+500x thousand dollars (a) Write a profit function for producing and selling x thousand notebook computers and indicate its domain. (b) Complete Table 13, computing profits to the nearest thousand dollars. (c) Plot the points in part (B) and sketch a graph of the profit function using these points.Muscle contraction. In a study of the speed of muscle contraction in frogs under various loads, British biophysicist A. W. Hill determined that the weight wingrams placed on the muscle and the speed of contraction vincentimeterspersecond are approximately related by an equation of the form w+av+b=c where a,b,andc are constants. Suppose that for a certain muscle, a=15,b=1,andc=90. Express v as a function of w. Find the speed of contraction if a weight of 16g is placed on the muscle.Politics. The percentage s of seats in the House of Representatives won by Democrats and the percentage v of votes cast for Democrats (when expressed as decimal fractions) are related by the equation 5v2s=1.40s1,0.28v0.68 (A) Express v as a function of s, and find the percentage of votes required for the Democrats to win 51 of the seats. (B) Express s as a function of v and find the percentage of seats won if Democrats receive 51 of the votes.Let fx=x2. (a) Graph y=fx+k for k=4,0,and2 simultaneously in the same coordinate system. Describe the relationship between the graph of y=fx and the graph of y=fx+k for any real number k. (b) Graph y=fx+h for h=4,0,and2 simultaneously in the same coordinate system. Describe the relationship between the graph of y=fx and the graph of y=fx+h for any real number h.(a) Graph y=Ax2forA=1,4and14 simultaneously in the same coordinate system. (b) Graph y=Ax2forA=1,4and14 simultaneously in the same coordinate system. (c) Describe the relationship between the graph of hx=x2 and the graph of Gx=Ax2 for any real number A.Explain why applying any of the graph transformations in the summary box to a linear function produces another linear function.Evaluate each basic elementary function at (A) x=729 (B) x=5.25 Round any approximate values to four decimal places.(A) How are the graphs of y=x+5 and y=x4 related to the graph of y=x ? Confirm your answer by graphing all three functions simultaneously in the same coordinate system. (B) How are the graphs of y=x+5 and y=x4 related to the graph of y=x ? Confirm your answer by graphing all three functions simultaneously in the same coordinate system.The graphs in Figure 5 are either horizontal or vertical shifts of the graph of fx=x3. Write appropriate equations for functions H,G,M,andN in terms of f.(a) How are the graphs of y=2x and y=0.5x related to the graph of y=x ? Confirm your answer by graphing all three functions simultaneously in the same coordinate system. (b) How is the graph of y=0.5x related to the graph of y=x ? Confirm your answer by graphing both functions in the same coordinate system.The graph of y=Gx in Figure 9 involves a reflection and a translation of the graph of y=x3. Describe how the graph of function G is related to the graph of y=x3 and find an equation of the function G.Graph the piecewise-defined function hx=2x+4if0x2x1ifx2 Trussville Utilities uses the rates shown in Table 2 to compute the monthly cost of natural gas for residential customers. Write a piecewise definition for the cost of consuming x CCF of natural gas and graph the function.In Problems 1-10, find the domain and range of each function fx=x24 In Problems 1-10, find the domain and range of each function fx=1+x In Problems 1-10, find the domain and range of each function fx=72x In Problems 1-10, find the domain and range of each function fx=x2+10 In Problems 1-10, find the domain and range of each function fx=8x In Problems 1-10, find the domain and range of each function fx=5x+3 In Problems 1-10, find the domain and range of each function fx=27+x3 In Problems 1-10, find the domain and range of each function fx=1520x In Problems 1-10, find the domain and range of each function fx=6x+9 In Problems 1-10, find the domain and range of each function fx=8+x3 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=fx+2 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=gx1 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=fx+2 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=gx1 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=gx3 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=fx+3 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=gx3 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=fx+3 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=fx In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=gx In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=0.5gx In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=2fx In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=2fx+1 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=0.5gx+3 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=2fx+1 In Problems 11-26, graph each of the functions using the graphs of functions f and g below. y=0.5gx+3 In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. gx=x+3 In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. hx=x5 In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. fx=x423 In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. mx=x+32+4 In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. fx=7x In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. gx=6+x3 In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. hx=3x In Problems 27-34, describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. mx=0.4x2 Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.Each graph in Problems 35-42 is the result of applying sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.In Problems 43-48, the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using 5x5 and 5y5. The graph of fx=x is shifted 2 units to the right and 3 units down.In Problems 43-48, the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using 5x5 and 5y5. The graph of fx=x3 is shifted 3 units to the left and 2 units up.In Problems 43-48, the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using 5x5 and 5y5. The graph of fx=x is reflected in the x axis and shifted to the left 3 unit.In Problems 43-48, the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using 5x5 and 5y5. The graph of fx=x is reflected in the x axis and shifted to the right 1 unit.In Problems 43-48, the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using 5x5 and 5y5. The graph of fx=x3 is reflected in the x axis and shifted 2 units to the right and down 1 unit.In Problems 43-48, the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using 5x5 and 5y5. The graph of fx=x2 is reflected in the x axis and shifted to the left 2 units and up 4 units.Graph each function in Problems 49-54. fx=22xifx2x2ifx2 Graph each function in Problems 49-54. gx=x+1ifx12+2xifx1 Graph each function in Problems 49-54. hx=5+0.5xif0x1010+2xifx10 Graph each function in Problems 49-54. hx=10+2xif0x2040+0.5xifx20 Graph each function in Problems 49-54. hx=2xif0x20x+20if20x400.5x+40ifx40 Graph each function in Problems 49-54. hx=4x+20if0x202x+60if20x100x+360ifx100 Each of the graphs in Problems 55-60 involves a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph.Each of the graphs in Problems 55-60 involves a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph.Each of the graphs in Problems 55-60 involves a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph.Each of the graphs in Problems 55-60 involves a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph.Each of the graphs in Problems 55-60 involves a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph.60E 61E 62E Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in Problems 61-66 to determine if reversing their order can produce a different result. Support your conclusions with specific examples and/or mathematical arguments. (The graph of y=fx is the reflection of y=fx in the y axis.) Vertical shift; reflection in x axis Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in Problems 61-66 to determine if reversing their order can produce a different result. Support your conclusions with specific examples and/or mathematical arguments. (The graph of y=fx is the reflection of y=fx in the y axis.) Vertical shift; vertical stretch 65E 66E Price-demand. A retail chain sells bicycle helmets. The retail price px (in dollars) and the weekly demand x for a particular model are related by px=1154x9x289 (A) Describe how the graph of function p can be obtained from the graph of one of the basic functions in Figure 1 on page 58. (B) Sketch a graph of function p using part (A) as an aid.Price-supply. The manufacturer of the bicycle helmets in Problem 67 is willing to supply x helmets at a price of px as given by the equation px=4x9x289 (a) Describe how the graph of function p can be obtained from the graph of one of the basic functions in Figure 1 on page 58. (b) Sketch a graph of function p using part (A) as an aid.Hospital costs. Using statistical methods, the financial department of a hospital arrived at the cost equation Cx=0.00048x5003+60000100x1000 Where Cx is the cost in dollars for handling x case per month. (a) Describe how the graph of function C can be obtained from the graph of one of the basic functions in Figure 1 on page 58. (b) Sketch a graph of function C using part (A) and a graphing calculator as aids.Price-demand. A company manufactures and sells in-line skates. Its financial department has established the price demand function px=1900.013x10210x100 Where px is the price at which x thousand pairs of in-line skates can be sold. (a) Describe how the graph of function p can be obtained from the graph of one of the basic functions in Figure 1 on page 58. (b) Sketch a graph of function p using part (A) and a graphing calculator as aids.Electricity rates. Table 3 shows the electricity rates charged by Monroe Utilities in the summer months. The base is a fixed monthly charge, independent of the kWh (kilo watt hours) used during the month. (a) Write a piecewise definition of the monthly charge Sx for a customer who uses x kWh in a summer month. (b) Graph Sx.Electricity rates. Table 4 shows the electricity rates charged by Monroe Utilities in the winter months. (A) Write a piecewise definition of the monthly charge Wx for a customer who uses x kWh in a summer month. (B) Graph Wx.State income tax. Table 5 shows state income tax rates for married couples filing a joint return in Louisiana. (A) Write a piecewise definition for Tx, the tax due on a taxable income of x dollars. (B) Graph Tx. (C) Find the tax due on a taxable income of $55,000. Of $110,000.State income tax. Table 6 shows state income tax rates for individuals filing a return in Louisiana. (a) Write a piecewise definition for Tx, the tax due on a taxable income of x dollars. (b) Graph Tx. (c) Find the tax due on a taxable income of $32,000. Of $64,000 (d) Would it be better for a married couple in Louisiana with two equal incomes to file jointly or separately? Discuss.Human weight. A good approximation of the normal weight of a person 60 inches or taller but not taller than 80 inches is given by wx=5.5x220, where x is height in inches and wx is weight in pounds. (a) Describe how the graph of function w can be obtained from the graph of one of the basic functions in Figure 1, page 58. (b) Sketch a graph of function w using part (A) as an aid.Herpetology. The average weight of a particular species of snake is given by wx=463x3,0.2x0.8, where x is length in meters and wx is weight in grams. (a) Describe how the graph of function w can be obtained from the graph of one of the basic functions in Figure 1, page 58. (b) Sketch a graph of function w using part (A) as an aid.Safety research. Under ideal conditions, if a person driving a vehicle slams on the brakes and skids to a stop, the speed of the vehicle vx (in miles per hour) is given approximately by vx=Cx, where x is the length of skid marks (in feet) and C is a constant that depends on the road conditions and the weight of the vehicle. For a particular vehicle, vx=7.08xand4x144. (a) Describe how the graph of function v can be obtained from the graph of one of the basic functions in Figure 1, page 58. (b) Sketch a graph of function v using part (A) as an aid.Learning. A production analyst has found that on average it takes a new person Tx minutes to perform a particular assembly operation after x performances of the operation, where, Tx=10x3,0x125. (a) Describe how the graph of function T can be obtained from the graph of one of the basic functions in Figure 1, page 58. (b) Sketch a graph of function T using part (A) as an aid.Indicate how the graph of each function is related to the graph of the function hx=x2. Find the highest or lowest point, whichever exists, on each graph. (A) fx=x327=x26x+2 (B) gx=0.5x+22+3=0.5x2+2x+5 (C) mx=x42+3=x2+8x8 (D) nx=3x+121=3x26x4 A Graph y=Ax2 for A=1,4, and 14 simultaneously in the same coordinate system. B Graph y=Ax2 for A=1,4, and 14 simultaneously in the same coordinate system. C Describe the relationship between the graph of hx=x2 and the graph of Gx=Ax2 for any real number A.(a) Sketch a graph of gx=2x25x5 in a rectangular coordinate system. (b) Find xandy intercepts algebraically to four decimal places (c) Graph gx=2x25x5 in a standard viewing window (d) Find the xandy intercepts to four decimal places using TRACE and the ZERO command on your graphing calculator.Given the quadratic function fx=0.25x22x+2 (a) Find the vertex form for f (b) Find the vertex and the maximum of minimum. State the graph of f (c) Describe how the graph of function f can be obtained from the graph of gx=x2 using transformations (d) Sketch a graph of function f in a rectangular coordinate system (e) Graph function f using a suitable viewing window (f) Find the vertex and the maximum of minimum using the appropriate graphing calculator command.The financial department in example 3, using statistical and analytical techniques (see Matched Problem 7 in Section 2.1 ), arrived at the cost function. cx=156+19.7x Cost function Where Cx is the cost for manufacturing and selling x million cameras. (a) Using the revenue function from example 3 and the preceding cost function write an equation for the profit function (b) Find the value of x to the nearest thousand cameras that will generate the maximum profit. What is the maximum profit to the nearest thousand dollars? Solve the problem algebraically by completing the square (c) What is the wholesale price per camera that generates the maximum profit? (d) Graph the profit function using an appropriate viewing window. (e) Find the output to the nearest thousand cameras that will generate the maximum profit. What is the maximum profit to the nearest thousand dollars? Solve the problem graphically using the maximum command.Use the profit equation from matched problem 3 : Px=RxCx=5x2+75.1x156Profitfunctiondomain:1x15 (a) Sketch a graph of the profit function in a rectangular coordinate system. (b) Break even points occur when Px=0 find the break-even points algebraically to the nearest thousand cameras (c) Plot the profit function in an appropriate viewing window. (d) Find the break-even point graphically to the nearest thousand cameras. (e) A loss occurs if Px0, and a profit occurs if Px0 for what values of x (to the nearest thousand cameras) will a loss occur? A profit?Refer to Table 1. Use quadratic regression to find the best model of the form y=ax2+bx+c for boat speed y (in miles per hour) as a function of engine speed x (in revolutions per minute). Estimate the boat speed (in miles per hour, to one decimal place) at an engine speed of 3,400 rpm.In problem 1-8, find the vertex form of each quadratic function by completing the square. fx=x210x In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx=x2+16x In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx=x2+20x+50 In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx=x212x8 In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx=2x2+4x5 In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx=3x2+18x+21 In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx=2x2+2x+1 In Problems 1-8, find the vertex form of each quadratic function by completing the square. fx= 5x2+15x11 In Problems 9-12, write a brief verbal description of the relation-ship between the graph of the indicated function and the graph of y=x2. fx=x24x+3 In Problems 9-12, write a brief verbal description of the relation-ship between the graph of the indicated function and the graph of y=x2. gx=x22x5 In Problems 9-12, write a brief verbal description of the relation-ship between the graph of the indicated function and the graph of y=x2. mx= x2+ 6x 4 In Problems 9-12, write a brief verbal description of the relation-ship between the graph of the indicated function and the graph of y=x2. nx= x2+8x 9 Match each equation with a graph of one of the functions f,g,m or n in the figure. (A) y=x+22+1 (B) y=x221 (C) y=x+221 (D) y=x22+1 Match each equation with a graph of one of the functions f,g,m,orn in the figure. (A) y=x324 (B) y=x+32+4 (C) y=x32+4 (D) y=x+324 For the functions indicated in Problems 15-18, find each of the following to the nearest integer by referring to the graphs for Problems 13 and 14. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function n in the figure for Problem 13 For the functions indicated in Problems 15-18, find each of the following to the nearest integer by referring to the graphs for Problems 13 and 14. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function m in the figure for Problem 14 For the functions indicated in Problems 15-18, find each of the following to the nearest integer by referring to the graphs for Problems 13 and 14. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function f in the figure for Problem 13 For the functions indicated in Problems 15-18, find each of the following to the nearest integer by referring to the graphs for Problems 13 and 14. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function g in the figure for Problem 14 In Problems 19-22, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range fx=x32+2 In Problems 19-22, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range gx=x+22+3 In Problems 19-22, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range mx=x+122 In Problems 19-22, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range nx=x423 In Problems 23-26, write an equation for each graph in the form y=axh2+k where a is either 1 or 1 and h and k are integers.In Problems 23-26, write an equation for each graph in the form y=axh2+k where a is either 1 or 1 and h and k are integers.In Problems 23-26, write an equation for each graph in the form y=axh2+k where a is either 1 or 1 and h and k are integers.In Problems 23-26, write an equation for each graph in the form y=axh2+k where a is either 1 or 1 and h and k are integers.Problems 27-32, find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range fx=x28x+12 Problems 27-32, find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range gx=x26x+5 Problems 27-32, find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range rx=4x2+16x15 Problems 27-32, find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range sx=4x28x3 Problems 27-32, find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range ux=0.5x22x+5 Problems 27-32, find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range vx=0.5x2+4x+10 Let fx=0.3x2x8. Solve each equation graphically to two decimal places. (A) fx=4 (B) fx=1 (C) fx=9 Let gx=0.6x2+3x+4. Solve each equation graphically to two decimal places (A) gx=2 (B) gx=5 (C) gx=8 Let fx=125x6x2. Find the maximum value of f to four decimal places graphically.Let fx=100x7x210. Find the maximum value of f to four decimal places graphically.In problem 37-40, first write each function in vertex form then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range gx=0.25x21.5x7 In problem 37-40, first write each function in vertex form then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range mx=0.20x21.6x1 In problem 37-40, first write each function in vertex form then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range fx=0.12x2+0.96x+1.2 In problem 37-40, first write each function in vertex form then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range nx=0.15x20.90x+3.3 In Problems 41-44, use interval notation to write the solution set of the inequality. x3x+50 In Problems 41-44, use interval notation to write the solution set of the inequality. x+6x30 In Problems 41-44, use interval notation to write the solution set of the inequality. x2+x60 In Problems 41-44, use interval notation to write the solution set of the inequality. x2+7x+120 Solve Problems 45-50, graphically to two decimal places using a graphing calculator 25xx2=0 Solve Problems 45-50, graphically to two decimal places using a graphing calculator 7+3x2x2=0 Solve Problems 45-50, graphically to two decimal places using a graphing calculator 1.9x21.5x5.60 Solve Problems 45-50, graphically to two decimal places using a graphing calculator 3.4+2.9x1.1x20 Solve Problems 45-50, graphically to two decimal places using a graphing calculator 2.8+3.1x0.9x20 Solve Problems 45-50, graphically to two decimal places using a graphing calculator 1.8x23.1x4.90 Given that f is a quadratic function with minimum fx=f2=4 find the axis, vertex, range and x intercepts.Given that f is a quadratic function with maximum fx=f3=5 find the axis, vertex, range and y intercepts.In Problems 53-56, (A) Graph f and g in the same coordinate system. (B) Solve fx=gx algebraically to two decimal places. (C) Solve fxgx using parts A and B (D) Solve fxgx using parts A and B fx=0.4xx10gx=0.3x+50x10 In Problems 53-56, (A) Graph f and g in the same coordinate system. (B) Solve fx=gx algebraically to two decimal places. (C) Solve fxgx using parts A and B (D) Solve fxgx using parts A and B fx=0.7xx7gx=0.5x+3.50x7 In Problems 53-56, (A) Graph f and g in the same coordinate system. (B) Solve fx=gx algebraically to two decimal places. (C) Solve fxgx using parts A and B (D) Solve fxgx using parts A and B fx=0.9x2+7.2xgx=1.2x+5.50x8 In Problems 53-56, (A) Graph f and g in the same coordinate system. (B) Solve fx=gx algebraically to two decimal places. (C) Solve fxgx using parts A and B (D) Solve fxgx using parts A and B fx=0.7x2+6.3xgx=1.1x+4.80x9 How can you tell from the graph of a quadratic function whether it has exactly one real zero?How can you tell from the graph of a quadratic function whether it has no real zeroes?How can you tell from the standard form y=ax2+bx+c whether a quadratic functiohn has two real zeroes?How can you tell from the standard form y=ax2+bx+c whether a quadratic form has one real zero?How can you tell from the vertex form y=axh2+k whether a quadratic function has no real zeroes?How can you tell from the vertex form y=axh2+k whether a quadratic function has two real zeroes?In problem 63 and 64 assume that a,b,c,h,andk are constants with a0 such that ax2+bx+c=axh2+k for all the real numbers x. Show that h=b2a.In problem 63 and 64 assume that a,b,c,h,andk are constants with a0 such that ax2+bx+c=axh2+k for all the real numbers x. Show that k=4acb24a.Tire mileage: An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles) A mathematical model for the data is given by fx=0.518x2+33.3x481 (A) Complete the following table. Round values of fx to one decimal place (B) Sketch the graph of f and the mileage data in the same coordinate system. (C) Use the modeling function fx to estimate the mileage for a tire pressure of 31lbs/sqin. and for 35lbs/sqin. Round answers to two decimal places. (D) Write a brief description of the relationship between tire pressure and mileage.Automobile production. The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market. A mathematical model for this data is given by fx=0.0117x2+0.32x+17.9 where x=0 corresponds to 1980. (A) Complete the following table. Round values of f(x) to one decimal place. (B) Sketch the graph of f and the market share data in the same coordinate system. (C) Use values of the modeling function f to estimate Ford’s market share in 2025 and in 2028. (D) Write a brief verbal description of Ford’s market share from 1985to2015.Tire mileage. Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on tire mileage in Problem 65 is fx=0.518x2+33.3x481 Automobile production. Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on market share in Problem 66 is fx=0.0117x2+0.32x+17.9 Revenue. The marketing research department for a company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions. px=753xPricedemandfunctionRx=xpx=x753xRevenuefunction Where px is the wholesale price in dollars at which x million chips can be sold, and Rx is in millions of dollars. Both functions have domain 1x20 (A) Sketch a graph of the revenue function in a rectangular coordinate system. (B) Find the value of x that will produce the maximum revenue. What is the maximum revenue? (C) What is the wholesale price per chip that produces the maximum revenue?70E Break-even analysis. Use the revenue function from Problem 69 and the given cost function: Rx=x753xRevenuefunctionCx=125+16xCostfunction where x is in millions of chips, and Rx and Cx are in millions of dollars. Both functions have domain 1x20. (A) Sketch a graph of both functions in the same rectangular coordinate system. (B) Find the break-even points to the nearest thousand chips. (C) For what values of x will a loss occur? A profit?Break-even analysis. Use the revenue function from Problem 70 and the given cost function: Rx=x2,00060xRevenuefunctionCx=4,000+500xCostfunction where x is millions of computers, and Cx and Rx are in thousands of dollars. Both functions have domain 1x25. (A) Sketch a graph of both functions in the same rectangular coordinate system. (B) Find the break-even points. (C) For what values of x will a loss occur? A profit?Profit-loss analysis. Use the revenue cost and cost function from problem 71 : Rx=x753xRevenuefunctionCx=125+16xCostfunction where x is in millions of chips, and Rx and Cx are in millions of dollars. Both functions have domain 1x20. (A) Form a profit function P, and graph R,C,andP in the same rectangular coordinate system. (B) Discuss the relationship between the intersection points of the graphs of R and C and the intercepts of P. (C) Find the x intercepts of P and the break-even points to the nearest thousand chips. (D) Find the value of x (to the nearest thousand chips) that produces the maximum profit. Find the maximum profit (to the nearest thousand dollars), and compare with problem 69B.Profit-loss analysis. Use the revenue function from Problem 70 and the given cost function: Rx=x2,00060xRevenuefunctionCx=4,000+500xCostfunction where x is thousands of computers, and RxandCx are in thousands of dollars. Both functions have domain 1x25. (A) Form a profit function P, and graph R,C,andP in the same rectangular coordinate system. (B) Discuss the relationship between the intersection points of the graphs of RandC and the x intercepts of P. (C) Find the x intercepts of P and the break-even points. (D) Find the value of x that produces the maximum profit. Find the maximum profit and compare with Problem 70B.Medicine. The French physician Poiseuille was the first to discover that blood flows faster near the center of an artery than near the edge. Experimental evidence has shown that the rate of flow v (in centimeters per second) at a point x centimeters from the center of an artery (see the figure) is given by v=fx=1,0000.04x20x0.2 Find the distance from the center that the rate of flow is 20 centimeters per second. Round answer to two decimal places.Medicine. Refer to Problem 75. Find the distance from the center that the rate of flow is 30 centimeters per second. Round answer to two decimal places.Outboard motors. The table gives performance data for a boat powered by an Evinrude outboard motor. Find a quadratic regression model y=ax2+bx+c for boat speed y (in miles per hour) as a function of engine speed (in revolutions per minute). Estimate the boat speed at an engine speed of 3,100 revolutions per minute.Outboard motors. The table gives performance data for a boat powered by an Evinrude outboard motor. Find a quadratic regression model y=ax2+bx+c for fuel consumption y (in miles per gallon) as a function of engine speed (in revolutions per minute). Estimate the fuel consumption at an engine speed of 2,300 revolutions per minute.A function f is bounded if the entire graph of f lies between two horizontal lines. The only polynomials that are bounded are the constant functions, but there are many rational functions that are bounded. Give an example of a bounded rational function, with domain the set of all real numbers, that is not a constant function.The data in Table 2 give the average weights of pike for certain lengths. Use a cubic regression polynomial to model the data. Estimate (to the nearest ounce) the weights of pike of lengths 39,40,41,42,and43 inches, respectively.Given the rational function gx=3x+3x29 (A) Find the domain. (B) Find the x and y intercepts. (C) Find the equations of all vertical asymptotes. (D) If there is a horizontal asymptote, find its equations. (E) Using the information from parts AD and additional points as necessary, sketch a graph of g.Find the vertical and horizontal asymptotes of a rational function. fx=x34xx2+5x Repeat Example 4 for Nt=25t+5t+5t0.In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=7x+21 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=x25x+6 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=x2+9x+20 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=303x In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=x2+2x6+3x4+15 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=5x6+x4+4x8+10 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=x2x+63 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=x52x+72 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=x225x3+83 In Problems 1-10, for each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercept fx=2x52x294 Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?Each graph in Problems 11-18 is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?What is the maximum number of x intercepts that a polynomial of degree 10 can have?What is the maximum number of x intercepts that a polynomial of degree 7 can have?What is the minimum number of x intercepts that a polynomial of degree 9 can have? Explain.What is the minimum number of x intercepts that a polynomial of degree 6 can have? Explain.For each rational function in Problems 23-28, (A) Find the intercepts for the graph. (B) Determine the domain. (C) Find any vertical or horizontal asymptotes for the graph. (D) Sketch any asymptotes as dashed lines. Then sketch a graph of y=fx fx=x+2x2 For each rational function in Problems 23-28, (A) Find the intercepts for the graph. (B) Determine the domain. (C) Find any vertical or horizontal asymptotes for the graph. (D) Sketch any asymptotes as dashed lines. Then sketch a graph of y=fx fx=x3x+3 For each rational function in Problems 23-28, (A) Find the intercepts for the graph. (B) Determine the domain. (C) Find any vertical or horizontal asymptotes for the graph. (D) Sketch any asymptotes as dashed lines. Then sketch a graph of y=fx fx=3xx+2 For each rational function in Problems 23-28, (A) Find the intercepts for the graph. (B) Determine the domain. (C) Find any vertical or horizontal asymptotes for the graph. (D) Sketch any asymptotes as dashed lines. Then sketch a graph of y=fx fx=2xx3

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