Precalculus (10th Edition)
Precalculus (10th Edition)
10th Edition
ISBN: 9780321979070
Author: Michael Sullivan
Publisher: PEARSON
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 3.1, Problem 38AYU

Phone Charges The monthly cost C , in dollars, for calls from the United States to Germany on a certain wireless plan is modelled by the function C ( x ) = 0.26 x + 5 , where x is the number of minutes used.

What is the cost if you talk on the phone 50 minutes?

Suppose that your monthly bill is $ 21.64. How many minutes did you use the phone?

Suppose that you budget $ 50 per month for calls to Germany, What is the maximum number of minutes that you can talk?

What is the domain of C if there are 30 days in the month?

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Chapter 3 Solutions

Precalculus (10th Edition)

Ch. 3.1 - Graph y=x21Ch. 3.1 - Find the slope of the line joining the points (...Ch. 3.1 - Prob. 3AYUCh. 3.1 - Solve: 6x900=15x+2850 . (pp. A44-A46)Ch. 3.1 - Prob. 5AYUCh. 3.1 - Prob. 6AYUCh. 3.1 - For the graph of the linear function f( x )=mx+b ,...Ch. 3.1 - If the slope m of the graph of a linear function...Ch. 3.1 - True or False The slope of a nonvertical line is...Ch. 3.1 - True or False The average rate of change of f( x...
Ch. 3.1 - What is the only type of function that has a...Ch. 3.1 - A car has 12,500 miles on its odometer. Say the...Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - Suppose that f( x )=4x1 and g(x)=2x+5 . a. Solve...Ch. 3.1 - Suppose that f( x )=3x+5 and g(x)=2x+15 . a. Solve...Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - Prob. 37AYUCh. 3.1 - Phone Charges The monthly cost in dollars, for...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Taxes The functionrepresents the tax bill of a...Ch. 3.1 - Luxury Tax In 2011, major league baseball signed a...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Cost Function The simplest cost function is the...Ch. 3.1 - Cost function Refer to problem 49. Suppose that...Ch. 3.1 - Prob. 49AYUCh. 3.1 - International Call Plan A cell phone company...Ch. 3.1 - Prob. 51AYUCh. 3.1 - Developing a Linear Model from Data The following...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Under what circumstances is a linear function f( x...Ch. 3.1 - Explain how the graph of f( x )=mx+b can be used...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.2 - Plot the points ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 )...Ch. 3.2 - Find an equation of the line containing the points...Ch. 3.2 - A _____________ is used to help us to see what...Ch. 3.2 - True or False The correlation coefficient is a...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - Candy The following data represent the weight (in...Ch. 3.2 - Prob. 18AYUCh. 3.2 - Video Games and Grade-Point Average Professor...Ch. 3.2 - Prob. 20AYUCh. 3.2 - Flight Time and Ticket Price The following data...Ch. 3.2 - Material Age versus Down Syndrome A biologist...Ch. 3.2 - Fine the line of the best fit for order pairs...Ch. 3.2 - What does a correlation coefficient of 0 imply?Ch. 3.2 - Explain why it does not make sense to interpret...Ch. 3.2 - Refer to Problem 19. Solve G( h )=0 . Provide an...Ch. 3.2 - Find an equation for the line containing the...Ch. 3.2 - Find the domain of f( x )= x1 x 2 25 .Ch. 3.2 - For f(x)=5x8 and g(x)= x 2 3x+4 , find (gf)(x) .Ch. 3.2 - Write the function whose graph is the graph of y=...Ch. 3.3 - List the intercepts of the equation y= x 2 9 ....Ch. 3.3 - Prob. 2AYUCh. 3.3 - To complete the square of x 2 5x , you add the...Ch. 3.3 - To graph y= (x4) 2 you shift the graph of y= x 2...Ch. 3.3 - The graph of a quadratic function is called a(n)...Ch. 3.3 - The vertical line passing through the vertex of a...Ch. 3.3 - The x-coordinate of the vertex of f( x )=a x 2...Ch. 3.3 - True or False The graph of f( x )=2 x 2 +3x4 opens...Ch. 3.3 - True or False The y-coordinate of the vertex of f(...Ch. 3.3 - True or False If the discriminant b 2 4ac=0 , the...Ch. 3.3 - If b 2 4ac0 , which of the following conclusions...Ch. 3.3 - If the graph of f( x )=a x 2 +bx+c,a0 , has a...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - Prob. 55AYUCh. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - Prob. 59AYUCh. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - Prob. 61AYUCh. 3.3 - Prob. 62AYUCh. 3.3 - In problem, graph each function.Determine the...Ch. 3.3 - In problem, graph each function.Determine the...Ch. 3.3 - In problem, graph each function.Determine the...Ch. 3.3 - In problem 6370, (a) graph each function. (b)...Ch. 3.3 - In problem 6370, (a) graph each function. (b)...Ch. 3.3 - In problem 6370, (a) graph each function. (b)...Ch. 3.3 - In problem 6370, (a) graph each function. (b)...Ch. 3.3 - In problem, graph each function.Determine the...Ch. 3.3 - The graph of the function f( x )=a x 2 +bx+c has...Ch. 3.3 - The graph of the function f(x)=a x 2 +bx+c has...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Suppose that f(x)= x 2 +4x21 . (a) What is the...Ch. 3.3 - Suppose that f( x )= x 2 +2x8 . (a) What is the...Ch. 3.3 - Prob. 83AYUCh. 3.3 - Prob. 84AYUCh. 3.3 - Maximizing Revenue Suppose that the manufacturer...Ch. 3.3 - Prob. 86AYUCh. 3.3 - Minimizing Marginal Cost The marginal cost of a...Ch. 3.3 - Minimizing Marginal Cost (See Problem 91.) The...Ch. 3.3 - Business The monthly revenue R achieved by selling...Ch. 3.3 - Business The daily revenue R achieved by selling x...Ch. 3.3 - Stopping Distance An accepted relationship between...Ch. 3.3 - Prob. 92AYUCh. 3.3 - Prob. 93AYUCh. 3.3 - Make up a quadratic function that opens down and...Ch. 3.3 - Prob. 95AYUCh. 3.3 - Prob. 96AYUCh. 3.3 - Prob. 97AYUCh. 3.3 - Prob. 98AYUCh. 3.3 - Prob. 99AYUCh. 3.3 - What are the possibilities for the number of times...Ch. 3.3 - Prob. 101AYUCh. 3.3 - Prob. 102AYUCh. 3.3 - Prob. 103AYUCh. 3.3 - Prob. 104AYUCh. 3.4 - Translate the following sentence into a...Ch. 3.4 - Prob. 2AYUCh. 3.4 - Prob. 3AYUCh. 3.4 - Prob. 4AYUCh. 3.4 - Prob. 5AYUCh. 3.4 - Prob. 6AYUCh. 3.4 - Enclosing a Rectangular Field David has 400 yards...Ch. 3.4 - Enclosing a Rectangular Field Beth has 3000 feet...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Analyzing the motion of a Projectile A projectile...Ch. 3.4 - Analyzing the motion of a Projectile A projectile...Ch. 3.4 - Suspension Bridge A suspension bridge with weight...Ch. 3.4 - Architecture A parabolic arch has a span of 120...Ch. 3.4 - Constructing Rain Gutters A rain gutter is to be...Ch. 3.4 - Norman Windows A Norman window has the shape of a...Ch. 3.4 - Constructing a Stadium A track-and-field playing...Ch. 3.4 - Architecture A special window has the shape of a...Ch. 3.4 - Height of a Rail A shot-putter throws a hall at an...Ch. 3.4 - Prob. 20AYUCh. 3.4 - Prob. 21AYUCh. 3.4 - Prob. 22AYUCh. 3.4 - Prob. 23AYUCh. 3.4 - Prob. 24AYUCh. 3.4 - Life Cycle Hypothesis An individual’s income...Ch. 3.4 - Prob. 27AYUCh. 3.4 - Which Model? An engineer collects the following...Ch. 3.4 - Which Model? The following data represent the...Ch. 3.4 - Which Model? A cricket makes a chirping noise by...Ch. 3.4 - Prob. 31AYUCh. 3.4 - Prob. 32AYUCh. 3.4 - Prob. 33AYUCh. 3.4 - Prob. 34AYUCh. 3.4 - Prob. 35AYUCh. 3.5 - Solve the inequality 3x27 .Ch. 3.5 - Write (2,7] using inequality notation.Ch. 3.5 - (a) f( x )0 (b) f( x )0Ch. 3.5 - (a) g( x )0 (b) g( x )0Ch. 3.5 - (a) g( x )f( x ) (b) f( x )g( x )Ch. 3.5 - (a) f( x )g( x ) (b) f( x )g( x )Ch. 3.5 - x 2 3x100Ch. 3.5 - x 2 +3x100Ch. 3.5 - x 2 4x0Ch. 3.5 - x 2 +8x0Ch. 3.5 - x 2 90Ch. 3.5 - x 2 10Ch. 3.5 - x 2 +x12Ch. 3.5 - x 2 +7x12Ch. 3.5 - 2 x 2 5x+3Ch. 3.5 - 6 x 2 6+5xCh. 3.5 - x 2 x+10Ch. 3.5 - x 2 +2x+40Ch. 3.5 - 4 x 2 +96xCh. 3.5 - 25 x 2 +1640xCh. 3.5 - 6( x 2 1 )5xCh. 3.5 - 2( 2 x 2 3x )9Ch. 3.5 - Prob. 23AYUCh. 3.5 - Prob. 24AYUCh. 3.5 - In Problems 2432, use the given functions f and g....Ch. 3.5 - Prob. 26AYUCh. 3.5 - Prob. 27AYUCh. 3.5 - Prob. 28AYUCh. 3.5 - Prob. 29AYUCh. 3.5 - Prob. 30AYUCh. 3.5 - Prob. 31AYUCh. 3.5 - Prob. 32AYUCh. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Revenue Suppose that the manufacturer of a gas...Ch. 3.5 - Revenue The John Deere company has found that the...Ch. 3.5 - Artillery A projectile Fired from the point ( 0,0...Ch. 3.5 - Runaway Car Using Hooke's Law, we can show that...Ch. 3.5 - Show that the inequality ( x4 ) 2 0 has exactly...Ch. 3.5 - Show that the inequality ( x2 ) 2 0 has one real...Ch. 3.5 - Explain why the inequality x 2 +x+10 has all real...Ch. 3.5 - Explain why the inequality x 2 x+10 has the empty...Ch. 3.5 - Explain the circumstances under which the...Ch. 3.5 - Determine the domain of f( x )= 102x .Ch. 3.5 - Consider the linear function f( x )= 2 3 x6 . (a)...Ch. 3.5 - Determine algebraically whether f( x )= x x 2 +9...Ch. 3.5 - Prob. 47AYUCh. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems: Find the slope and-intercept of each...Ch. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems 4 and 5, determine whether the...Ch. 3 - In Problems 4 and 5, determine whether the...Ch. 3 - In Problems, graph each quadratic function using...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems, graph each quadratic function using...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems 913, (a) graph each quadratic function...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 913, (a) graph each quadratic function...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems, determine whether the given quadratic...Ch. 3 - In Problems 18-19, solve each quadratic...Ch. 3 - In Problems 18-19, solve each quadratic...Ch. 3 - In Problems 19 and 20, find the quadratic function...Ch. 3 - 20. In Problems 20 and 21, find the quadratic...Ch. 3 - 22. Sales Commissions Bill has just been offered a...Ch. 3 - Prob. 22RECh. 3 - Landscaping A landscape engineer has 200 feet of...Ch. 3 - 24. Enclosing the Most Area with a Fence A farmer...Ch. 3 - Architecture A special window in the shape of a...Ch. 3 - 25. Minimizing Marginal Cost Callaway Golf Company...Ch. 3 - 26. Maximizing Area A rectangle has one vertex on...Ch. 3 - 27. Parabolic Arch Bridge A horizontal bridge is...Ch. 3 - 28. Bono Length Research performed at NASA, led by...Ch. 3 - 29. Advertising A small manufacturing firm...Ch. 3 - For the linear function f( x )=4x+3 , a. Find the...Ch. 3 - In Problems 2 and 3, find the intercepts, if any,...Ch. 3 - In Problemsand, find the intercepts, if any, of...Ch. 3 - Prob. 4CTCh. 3 - Graph f(x)= (x3) 2 2 using transformations.Ch. 3 - Consider the quadratic function Is the graph...Ch. 3 - Determine whether f( x )=-2 x 2 +12x+3 has a...Ch. 3 - Solve, x 2 10x+240 .Ch. 3 - The weekly rental cost of a 20-foot recreational...Ch. 3 - Find the distance between the points P=( 1,3 ) and...Ch. 3 - Prob. 2CRCh. 3 - Solve the inequality 5x+30 and graph the solution...Ch. 3 - Find the equation of the line containing the...Ch. 3 - Find the equation of the line perpendicular to the...Ch. 3 - Graph the equation x 2 + y 2 4x+8y5=0 .Ch. 3 - Does the following relation represent a function?...Ch. 3 - For the function f defined by f( x )= x 2 4x+1 ,...Ch. 3 - Find the domain of h(z)= 3z1 6z7 .Ch. 3 - Is the following graph the graph of a function?Ch. 3 - Consider the function f(x)= x x+4 . a. Is the...Ch. 3 - Is the function f(x)= x 2 2x+1 even, odd, or...Ch. 3 - Approximate the local maximum values and local...Ch. 3 - If f(x)=3x+5 and g(x)=2x+1 , a. Solve f(x)=g( x )...Ch. 3 - For the graph of the function f , a. Find the...

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