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All Textbook Solutions for Precalculus

In Problems 77-82, for the given functions fandg , (a) Graph fandg on the same Cartesian plane. (b) Solve f( x )=g( x ) . (c) Use the result of part (b) to label the points of intersection of the graphs of fandg . Shade the region for which f( x )g( x ) , that is, the region below f and above g . f( x )= x 2 +7x6;g( x )= x 2 +x6 Answer Problems 83 and 84 using the following: A quadratic function of the form f( x )=a x 2 +bx+c with b 2 4ac0 may also be written in the form f( x )=a(x r 1 )(x r 2 ) , where r 1 and r 2 are the x-intercepts of the graph of the quadratic function. (a) Find a quadratic function whose x-intercepts are 3 and 1 with a=1;a=2;a=2;a=5 . (b) How does the value of a affect the intercepts? (c) How does the value of a affect the axis of symmetry? (d) How does the value of a affect the vertex? (e) Compare the x-coordinate of the vertex with the midpoint of the x-intercepts . What might you conclude?Answer Problems 83 and 84 using the following: A quadratic function of the form f( x )=a x 2 +bx+c with b 2 4ac0 may also be written in the form f( x )=a(x r 1 )(x r 2 ) , where r 1 and r 2 are the x-intercepts of the graph of the quadratic function. (a) Find a quadratic function whose x-intercepts are 5 and 3 with a=1;a=2;a=2;a=5 . (b) How does the value of a affect the intercepts? (c) How does the value of a affect the axis of symmetry? (d) How does the value of a affect the vertex? (e) Compare the x-coordinate of the vertex with the midpoint of the x-intercepts . What might you conclude?Suppose that f(x)= x 2 +4x21 . (a) What is the vertex of f ? (b) What are the x-intercepts of the graph of f ? (c) Solve f(x)=21 for x . What points are on the graph of f ? (d) Use the information obtained in parts (a)(c) to graph f(x)= x 2 +4x21 .Suppose that f( x )= x 2 +2x8 . (a) What is the vertex of f ? (b) What are the x-intercepts of the graph of f ? (c) Solve f( x )=8 for x . What points are on the graph of f ? (d) Use the information obtained in parts (a)(c) to graph f( x )= x 2 +2x8 .Analyzing the Motion of a Projectile A projectile is fired from a cliff feet above the water at an inclination of to the horizontal, with a muzzle velocity of feet per second. The height of the projectile above the water is modeled by Where is the horizontal distance of the projectile from the face of the cliff. At what horizontal distance from the face of the cliff is the height of the projectile a maximum? Find the maximum height of the projectile. At what horizontal distance from the face of the cliff will the projectile strike the water? Graph the function ,. Use a graphing utility to verify the solutions found in parts and. When the height of the projectile is feet above the water, how far is it from the cliff ? Analyzing the Motion of a Projectile A projectile is fired at an inclination ofto the horizontal, with a muzzle velocity offeet per second. The heightof the projectile is modeled by Whereis the horizontal distance of the projectile from the firing point. At what horizontal distance from the firing point is the height of the projectile Find the maximum height of the projectile. At what horizontal distance from the firing point will the projectile strike the ground? Graph the function. Use a graphing utility to verify the results obtained in parts and. When the height of the projectile is feet above the ground, how far has it travelled horizontally? Maximizing Revenue Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R( p )=4 p 2 +4000p What unit price should be established for the dryer to maximize revenue? What is the maximum revenue?Maximizing Revenue A lawn mower manufacturer has found that the revenue, in dollars, from sales of zero-turn mowers is a function of the unit price,in dollars, that it charges. If the revenueis What unit priceshould be charged to maximize revenue? What is the maximum revenue? Minimizing Marginal Cost The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is 6.20 , it cost 6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C (in dollars) to produce x thousand digital music players is given by the function C(x)= x 2 140x+7400 (a) How many players should be produced to minimize the marginal cost? (b) What is the minimum marginal cost?Minimizing Marginal Cost (See Problem 91.) The marginal cost C (in dollars) of manufacturing x cell phones (in thousands) is given by C( x )=5 x 2 200x+4000 (a) How many cell phones should be manufactured to minimize the marginal cost? (b) What is the minimum marginal cost?Business The monthly revenue R achieved by selling x wristwatches is figured to be R( x )=75x0.2 x 2 . The monthly cost C of selling x wristwatches is C( x )=32x+1750 . (a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as P(x)=R( x )C( x ) . What is the profit function? (c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a)and(c) differ. Explain why a quadratic function is a reasonable model for revenue.Business The daily revenue R achieved by selling x boxes of candy is figured to be R( x )=9.5x0.04 x 2 . The daily cost C of selling x boxes of candy is C( x )=1.25x+250 . (a) How many boxes of candy must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as P(x)=R(x)C( x ) . What is the profit function? (c) How many boxes of candy must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a)and(c) differ. Explain why a quadratic function is a reasonable model for revenue.Stopping Distance An accepted relationship between stopping distance d(in feet) and the speed v of a car(in mph), is d=1.1v+0.06v2 on dry level concrete How many feet will it take a car traveling 45 mph to stop on dry level concrete? If an accident occurs 200 feet ahead of you, what is the maximum speed you can be traveling to avoid being involved?82AYU 83AYU 84AYU 85AYU 86AYU 87AYU 88AYU 89AYU 90AYU 91AYU 92AYU 1AYU 2AYU 3AYU 4AYU 5AYU 6AYU 7AYU 8AYU 9AYU 10AYU 11AYU 12AYU 13AYU 14AYU 15AYU 16AYU 17AYU 18AYU 19AYU 20AYU 21AYU 22AYU 23AYU 24AYU 25AYU 26AYU 27AYU 28AYU 29AYU 30AYU 31AYU Solve the inequality 3x27 .Write (2,7] using inequality notation.(a) f( x )0 (b) f( x )0 (a) g( x )0 (b) g( x )0 (a) g( x )f( x ) (b) f( x )g( x )(a) f( x )g( x ) (b) f( x )g( x )x 2 3x100 x 2 +3x100 x 2 4x0 x 2 +8x0 x 2 90 x 2 10 x 2 +x12 x 2 +7x12 2 x 2 5x+3 6 x 2 6+5x x 2 x+10 x 2 +2x+40 4 x 2 +96x 25 x 2 +1640x 6( x 2 1 )5x 2( 2 x 2 3x )9 23AYU 24AYU In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 1 g( x )=3x+3 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 +3 g( x )=3x+3 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 +1 g( x )=4x+1 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 +4 g( x )=x2 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 4 g( x )= x 2 +4 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 2x+1 g( x )= x 2 +1 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 x2 g( x )= x 2 +x2 In Problems 25-32, use the given functions f and g . (a) Solvef( x )=0 . (b) Solveg( x )=0 . (c) Solvef( x )=g( x ) . (d) Solvef( x )0 . (e) Solveg( x )0 . (f) Solvef( x )g( x ) . (g) Solvef( x )1 . f( x )= x 2 x+1 g( x )= x 2 +x+6 33AYU 34AYU 35AYU 36AYU 37AYU 38AYU 39AYU 40AYU 41AYU 42AYU 43AYU In Problems 14, determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. f(x)=4x53x2+5x2 In Problems 14, determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. f(x)=3x52x+1 In Problems 14, determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. f(x)=3x2+5x121 In Problems 14, determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. f(x)=3 In Problems , graph each function using transformation(shifting, compressing, stretching, and reflecting).Show all the stages. 5. 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE In Problems 1214, find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. R(x)=x+2x29 In Problems 1214, find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. R(x)=x2+4x2 In Problems , find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. 14. 22RE In Problems 1520, graph each rational function following the seven steps on page 211. R(x)=2x6x 24RE 25RE 26RE 27RE 28RE 29RE 30RE 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE 39RE 40RE 41RE 42RE 43RE 44RE 45RE 46RE 47RE 48RE 49RE 50RE 51RE 52RE 53RE 54RE 55RE 56RE 57RE 58RE 59RE 60RE 61RE 62RE 63RE 64RE 65RE 66RE 67RE 68RE 69RE 70RE 71RE 72RE 73RE 74RE 75RE 76RE 77RE 78RE 79RE 80RE 81RE 82RE 83RE 84RE 85RE 86RE 87RE 88RE 89RE 90RE 91RE Graph f(x)=(x3)42 using transformations.For the polynomial function , Determine the maximum number of real zeros that the function may have. List the potential rational zeros. Determine the real zeros of . Factor over the reals. Find the and intercepts of the graph of . Determine whether the graph crosses or touches the x –axis at each x –intercept. Find the power function that the graph of resembles for large value of . Put all the information together to obtain the graph of . Find the complex zeros of f(x)=x34x2+25x100. Solve in the complex number system. In problems 5 and 6, find the domain of each function. Find any horizontal, vertical, or oblique asymptotes. g(x)=2x214x+24x2+6x40 In problems and , find the domain of each function. Find any horizontal, vertical, or oblique asymptotes. Graph the function in Problem 6. Label all intercepts, vertical asymptotes, horizontal asymptotes, and oblique asymptotes.In Problems 8 and 9, write a function that meets the given condition. Fourth degree polynomial with real coefficients; zeros;2,0,3+i Rational function; asymptotes: , ; domain : Use the Intermediate Value Theorem to show that the function has at least one zero on the interval . Solve: Find the distance between the points and . Solve the inequality x2x and graph the solution set.Solve the inequality x23x4 and graph the solution set.Find a linear function with slope 3 that contains the point (1,4). Graph the function. Find the equation of the line parallel to the line and consisting the point. Express your answer in slope-intercept form, and graph the function. Graph the equation. Does the relation {(3, 6), (1, 3), (2, 5), (3, 8)} represent a function? Why or why not?Solve the equation x36x2+8x=0.Solve the inequality 3x+25x1 and graph the solution set.10CR For the equation y=x39x, determine the intercepts and test for symmetry.Find the equation of the line perpendicular to that contains the point. Is the following the graph of a function? Why or why not?For the function f(x)=x2+5x2, find f(3) f(x) f(x) f(3x) f(x+h)f(x)h, h0 Given the function f(x)=x+5x1 What is the domain of f? Is the point (2,6) on the graph of f? If x=3, what is f(x)? What point is on the graph of f? If f(x)=9, what is x? What point is on the graph of f? Is f a polynomial or a rational function?Graph the function f(x)=3x+7.Graph f(x)=2x24x+1 by determining whether its graph is concave up or concave down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. Find the average rate of change of from to . Use this result to find the equation of the secant line containing and . In parts (a) to (f), use the following graph, Find the intercepts Based on the graph, tell whether the graph is symmetric with respect to the x- axis, the y- axis, and/or the origin. Based on the graph, tell whether the function is even, odd, or neither. List the interval on which f is decreasing. List the number, if any, at which f has a local maximum. What are the local maximum values? List the number, if any, at which f has a local minimum. What are the local minimum values?Determine algebraically whether the function f(x)=5xx29 is even, odd, or neither. For the function Find the domain of . Locate any intercepts. Graph the function. Based on the graph, find the range. Graph the function f(x)=3(x+1)2+5 using transformations. Suppose that and . Find and state its domain. Find and its domain. Demand Equation The price (in dollars) and the quantity sold of certain product obey the demand equation , . Express the revenue as a function of . What is the revenue if units are sold? What quantity maximizes revenue? What is the maximum revenue? What price should the company charge to maximize revenue? The intercepts of the equation 9 x 2 +4y=36 are ______. (pp.18-19)Is the expression 4 x 3 3.6 x 2 2 a polynomial? If so, what is its degree? (pp. A22-A23)To graph y= x 2 4 , you would shift the graph of y= x 2 ______ a distance of ______ units. (pp. 106-114)4AYU 5AYU 6AYU The graph of every polynomial function is both _______ and _______.If r is a real zero of even multiplicity of a polynomial function f , then the graph of f _______ (crosses/touches) the x-axis at r .The graphs of power functions of the form f(x)= x n , where n is an even integer, always contain the points ________, _______, and ______.If r is a solution to the equation f(x)=0 , name three additional statements that can be made about f and r assuming f is a polynomial function.The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called ________.The graph of the function f(x)=3x4x3+5x22x7 resembles the graph of for large values of |x|.If f( x )=2 x 5 + x 3 5 x 2 +7 , then lim x f( x )= _____ and lim x f( x )= _____.14AYU In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. f(x)=4x+ x 3 In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. f( x )=5 x 2 +4 x 4 In Problems 1526, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, state why not. Write each polynomial in standard form. Then identify the leading term and the constant term. g(x)=2+3x25 In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. h(x)=3 1 2 x In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. f(x)=1 1 x In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. f(x)=x(x1)In Problems, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, state why not. Write each polynomial in standard form. Then identify the leading term and the constant term. 21. In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. h(x)= x ( x 1 )In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. F(x)=5 x 4 x 3 + 1 2 In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. F(x)= x 2 5 x 3 In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. G( x )=2 ( xl ) 2 ( x 2 +1)In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. G( x )=3 x 2 (x+2) 3 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= ( x+1 ) 4 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= ( x2 ) 5 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= x 5 3 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= x 4 +2 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= 1 2 x 4 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )=3 x 5 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= x 5 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= x 4 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= ( x1 ) 5 +2 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= ( x+2 ) 4 3 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )=2 ( x+1 ) 4 +1 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )= 1 2 ( x1 ) 5 2 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )=4 ( x2 ) 5 In Problems 29-42, use transformations of the graph of y= x 4 or y= x 5 to graph each function. f( x )=3 ( x+2 ) 4 In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: 1 , 1, 3; degree 3.In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: 2 , 2, 3; degree 3.In Problems 4148, find a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of the leading coefficients. Zeros: 5,0,6; degree 3 In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: 4 , 0, 2; degree 3.In Problems 4148, find a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of the leading coefficients. Zeros: 5,2,3,5; degree 4 In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: 3 , 1 , 2, 5; degree 4.In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: 1 , multiplicity 1; 3, multiplicity 2; degree 3.In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: 2 , multiplicity 2; 4, multiplicity 1; degree 3.In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f(x)=3( x7 ) ( x+3 ) 2 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )=4( x+4 ) ( x+3 ) 3 In Problems 5970, for each polynomial function: List each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. Determine the maximum number of turning points on the graph. Determine the end behaviour; that is, find the power function that the graph of f resembles for large values of |x|. f(x)=7(x2+4)2(x5)3 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )=2( x3 ) ( x 2 +4 ) 3 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )=2 ( x+ 1 2 ) 2 ( x+4 ) 3 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )= ( x 1 3 ) 2 ( x1 ) 3 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )= ( x5 ) 3 ( x+4 ) 2 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )= ( x+ 3 ) 2 ( x2 ) 4 In Problems 5970, for each polynomial function: List each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. Determine the maximum number of turning points on the graph. Determine the end behaviour; that is, find the power function that the graph of f resembles for large values of |x|. f(x)=12(2x2+9)2(x2+7)In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )=2 ( x 2 +3 ) 3 In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )=2 x 2 ( x 2 2 )In Problems 57-68, for each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of | x | . f( x )=4x( x 2 3 )In Problems 69-72, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.In Problems 69-72, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.In Problems 69-72, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.In Problems 69-72, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.In Problems 73-76, construct a polynomial function that might have the given graph. (More than one answer may be possible.)In Problems 73-76, construct a polynomial function that might have the given graph. (More than one answer may be possible.)In Problems 73-76, construct a polynomial function that might have the given graph. (More than one answer may be possible.)In Problems 73-76, construct a polynomial function that might have the given graph. (More than one answer may be possible.)69AYU 70AYU 71AYU 72AYU 73AYU 74AYU 75AYU

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