Calculus
Calculus
11th Edition
ISBN: 9781337275576
Author: Larson, Ron, Edwards, Bruce
Publisher: Cengage Learning,
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Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…
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Chapter P, Problem 40RE
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To calculate: What is the value of f(x)−f(1)x−1 of the given function expressed as f(x)=2x−6.

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For Exercise, fill in the blanks and determine an equation for f−1(x) mentally.If function f adds 6 to x, then f−1 _____ 6 from x. Function f is defined by f(x) = x+ 6, and function f−1 is defined by f−1(x) = _____.
Mathematically show that f(x) = 3x³ – x is an odd function. %3D
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Chapter P Solutions

Calculus

Ch. P.1 - Finding Intercepts Describe how to find the x- and...Ch. P.1 - CONCEPT CHECK Verifying Points of Intersection How...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Prob. 7ECh. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Prob. 10E
Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Approximating Solution Points Using Technology In...Ch. P.1 - Approximating Solution Points Using Technology In...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Prob. 22ECh. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Prob. 29ECh. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - Prob. 34ECh. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - Prob. 38ECh. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Prob. 43ECh. P.1 - Prob. 44ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 46ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 48ECh. P.1 - Prob. 49ECh. P.1 - Prob. 50ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 53ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 55ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection In Exercises 57-62,...Ch. P.1 - Prob. 61ECh. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection Using Technology In...Ch. P.1 - Prob. 64ECh. P.1 - Prob. 65ECh. P.1 - Finding Points of Intersection Using Technology In...Ch. P.1 - Modeling Data The table shows the Gross Domestic...Ch. P.1 - Prob. 68ECh. P.1 - Break-Even Point Find the sales necessary to break...Ch. P.1 - Using Solution Points For what values of k does...Ch. P.1 - EXPLORING CONCEPTS Using Intercepts Write an...Ch. P.1 - EXPLORING CONCEPTS Symmetry A graph is symmetric...Ch. P.1 - Prob. 73ECh. P.1 - HOW DO YOU SEE IT? Use the graphs of the two...Ch. P.1 - True or False ? In Exercises 75-78, determine...Ch. P.1 - Prob. 76ECh. P.1 - True or False? In Exercises 75-78, determine...Ch. P.1 - True or False? In Exercises 75-78, determine...Ch. P.2 - Slope-Intercept Form In the form y = mx + b, what...Ch. P.2 - Perpendicular Lines Is it possible for two lines...Ch. P.2 - Estimating Slope In Exercises 36, estimate the...Ch. P.2 - Prob. 4ECh. P.2 - Prob. 5ECh. P.2 - Prob. 6ECh. P.2 - Prob. 7ECh. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Sketching Lines In Exercises 13 and 14. sketch the...Ch. P.2 - Sketching Lines In Exercises 13 and 14, sketch the...Ch. P.2 - Prob. 15ECh. P.2 - Finding Points on a Line In Exercises 1518, use...Ch. P.2 - Prob. 17ECh. P.2 - Finding Points on a Line In Exercises 1518, use...Ch. P.2 - Finding an Equation of a Line In Exercises 19-24,...Ch. P.2 - Prob. 20ECh. P.2 - Prob. 21ECh. P.2 - Prob. 22ECh. P.2 - Prob. 23ECh. P.2 - Prob. 24ECh. P.2 - Prob. 25ECh. P.2 - Prob. 26ECh. P.2 - Prob. 27ECh. P.2 - Prob. 28ECh. P.2 - Prob. 29ECh. P.2 - Finding the Slope and y-Intercept In Exercises...Ch. P.2 - Prob. 31ECh. P.2 - Prob. 32ECh. P.2 - Prob. 33ECh. P.2 - Prob. 34ECh. P.2 - Sketching a Line in the Plane In Exercises 35-42,...Ch. P.2 - Prob. 36ECh. P.2 - Prob. 37ECh. P.2 - Prob. 38ECh. P.2 - Prob. 39ECh. P.2 - Prob. 40ECh. P.2 - Prob. 41ECh. P.2 - Prob. 42ECh. P.2 - Prob. 43ECh. P.2 - Prob. 44ECh. P.2 - Prob. 45ECh. P.2 - Prob. 46ECh. P.2 - Prob. 47ECh. P.2 - Prob. 48ECh. P.2 - Prob. 49ECh. P.2 - Prob. 50ECh. P.2 - Prob. 51ECh. P.2 - Prob. 52ECh. P.2 - Writing an Equation in General Form In Exercises...Ch. P.2 - Prob. 54ECh. P.2 - Writing an Equation in General Form In Exercises...Ch. P.2 - Prob. 56ECh. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Prob. 63ECh. P.2 - Prob. 64ECh. P.2 - Prob. 65ECh. P.2 - Prob. 66ECh. P.2 - Prob. 67ECh. P.2 - Analyzing a Line A line is represented by the...Ch. P.2 - Tangent Line Find an equation of the line tangent...Ch. P.2 - Prob. 70ECh. P.2 - Finding Points of Intersection Find the...Ch. P.2 - Prob. 72ECh. P.2 - Prob. 73ECh. P.2 - Prob. 74ECh. P.2 - Apartment Rental A real estate office manages an...Ch. P.2 - Prob. 76ECh. P.2 - Prob. 77ECh. P.2 - Prob. 78ECh. P.2 - Prob. 79ECh. P.2 - Prob. 80ECh. P.2 - Prob. 81ECh. P.2 - Prob. 82ECh. P.2 - Prob. 83ECh. P.2 - Prob. 84ECh. P.2 - Prob. 85ECh. P.2 - True or False? In Exercises 85 and 86, determine...Ch. P.3 - Writing Describe how a relation and a function are...Ch. P.3 - Prob. 2ECh. P.3 - Prob. 3ECh. P.3 - Prob. 4ECh. P.3 - Prob. 5ECh. P.3 - Prob. 6ECh. P.3 - Evaluating a Function In Exercises 5-12, evaluate...Ch. P.3 - Prob. 8ECh. P.3 - Prob. 9ECh. P.3 - Prob. 10ECh. P.3 - Prob. 11ECh. P.3 - Prob. 12ECh. P.3 - Prob. 13ECh. P.3 - Prob. 14ECh. P.3 - Prob. 15ECh. P.3 - Finding the Domain and Range of a Function In...Ch. P.3 - Prob. 17ECh. P.3 - Finding the Domain and Range of a Function In...Ch. P.3 - Finding the Domain and Range of a Function In...Ch. P.3 - Prob. 20ECh. P.3 - Prob. 21ECh. P.3 - Prob. 22ECh. P.3 - Prob. 23ECh. P.3 - Prob. 24ECh. P.3 - Prob. 25ECh. P.3 - Prob. 26ECh. P.3 - Prob. 27ECh. P.3 - Prob. 28ECh. P.3 - Prob. 29ECh. P.3 - Prob. 30ECh. P.3 - Prob. 31ECh. P.3 - Sketching a Graph of a Function In Exercises...Ch. P.3 - Prob. 33ECh. P.3 - Prob. 34ECh. P.3 - Prob. 35ECh. P.3 - Prob. 36ECh. P.3 - Prob. 37ECh. P.3 - Prob. 38ECh. P.3 - Prob. 39ECh. P.3 - Using the Vertical Line Test In Exercises 39-42,...Ch. P.3 - Prob. 41ECh. P.3 - Prob. 42ECh. P.3 - Prob. 43ECh. P.3 - Prob. 44ECh. P.3 - Prob. 45ECh. P.3 - Prob. 46ECh. P.3 - Prob. 47ECh. P.3 - Prob. 48ECh. P.3 - Prob. 49ECh. P.3 - Prob. 50ECh. P.3 - Prob. 51ECh. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Prob. 53ECh. P.3 - Prob. 54ECh. P.3 - Prob. 55ECh. P.3 - Prob. 56ECh. P.3 - Sketching Transformations Use the graph of f shown...Ch. P.3 - Sketching Transformations Use the graph of f shown...Ch. P.3 - Prob. 59ECh. P.3 - Prob. 60ECh. P.3 - Prob. 61ECh. P.3 - Prob. 62ECh. P.3 - Finding Composite Functions In Exercises 63-66,...Ch. P.3 - Prob. 64ECh. P.3 - Prob. 65ECh. P.3 - Prob. 66ECh. P.3 - Evaluating Composite Functions Use the graphs of f...Ch. P.3 - Ripples A pebble is dropped into a calm pond,...Ch. P.3 - Prob. 69ECh. P.3 - Prob. 70ECh. P.3 - Think About It In Exercises 71 and 72, find the...Ch. P.3 - Prob. 72ECh. P.3 - Ever, and Odd Functions The graphs of f, g, and h...Ch. P.3 - Prob. 74ECh. P.3 - Prob. 75ECh. P.3 - Prob. 76ECh. P.3 - Prob. 77ECh. P.3 - Prob. 78ECh. P.3 - Prob. 79ECh. P.3 - Prob. 80ECh. P.3 - Prob. 81ECh. P.3 - Prob. 82ECh. P.3 - Prob. 83ECh. P.3 - Prob. 84ECh. P.3 - Prob. 85ECh. P.3 - Prob. 86ECh. P.3 - Domain Find the value of c such that the domain of...Ch. P.3 - Domain Find all values of c such that the domain...Ch. P.3 - Prob. 89ECh. P.3 - Prob. 90ECh. P.3 - Prob. 91ECh. P.3 - Prob. 92ECh. P.3 - Graphical Reasoning An electronically controlled...Ch. P.3 - HOW DO YOU SEE IT? Water runs into a vase of...Ch. P.3 - Prob. 95ECh. P.3 - Prob. 96ECh. P.3 - Proof Prove that the function is odd...Ch. P.3 - Proof Prove that the function is even....Ch. P.3 - Prob. 99ECh. P.3 - Prob. 100ECh. P.3 - Length A right triangle is formed in the first...Ch. P.3 - Volume An open box of maximum volume is to be made...Ch. P.3 - Prob. 103ECh. P.3 - Prob. 104ECh. P.3 - Prob. 105ECh. P.3 - Prob. 106ECh. P.3 - Prob. 107ECh. P.3 - Prob. 108ECh. P.3 - Prob. 109ECh. P.3 - Prob. 110ECh. P.4 - Coterminal Angles Explain how to find coterminal...Ch. P.4 - Prob. 2ECh. P.4 - Prob. 3ECh. P.4 - Prob. 4ECh. P.4 - Prob. 5ECh. P.4 - Prob. 6ECh. P.4 - Prob. 7ECh. P.4 - Prob. 8ECh. P.4 - Prob. 9ECh. P.4 - Prob. 10ECh. P.4 - Prob. 11ECh. P.4 - Prob. 12ECh. P.4 - Prob. 13ECh. P.4 - Prob. 14ECh. P.4 - Prob. 15ECh. P.4 - Prob. 16ECh. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Prob. 18ECh. P.4 - Prob. 19ECh. P.4 - Prob. 20ECh. P.4 - Prob. 21ECh. P.4 - Prob. 22ECh. P.4 - Prob. 23ECh. P.4 - Prob. 24ECh. P.4 - Prob. 25ECh. P.4 - Prob. 26ECh. P.4 - Prob. 27ECh. P.4 - Prob. 28ECh. P.4 - Prob. 29ECh. P.4 - Prob. 30ECh. P.4 - Prob. 31ECh. P.4 - Prob. 32ECh. P.4 - Prob. 33ECh. P.4 - Prob. 34ECh. P.4 - Prob. 35ECh. P.4 - Prob. 36ECh. P.4 - Prob. 37ECh. P.4 - Solving a Trigonometric Equation In Exercises...Ch. P.4 - Prob. 39ECh. P.4 - Prob. 40ECh. P.4 - Prob. 41ECh. P.4 - Prob. 42ECh. P.4 - Airplane Ascent An airplane leaves the runway...Ch. P.4 - Height of a Mountain While traveling across flat...Ch. P.4 - Prob. 45ECh. P.4 - Prob. 46ECh. P.4 - Prob. 47ECh. P.4 - Prob. 48ECh. P.4 - Prob. 49ECh. P.4 - Prob. 50ECh. P.4 - Prob. 51ECh. P.4 - Prob. 52ECh. P.4 - Prob. 53ECh. P.4 - Prob. 54ECh. P.4 - Prob. 55ECh. P.4 - Prob. 56ECh. P.4 - Prob. 57ECh. P.4 - Prob. 58ECh. P.4 - Prob. 59ECh. P.4 - Prob. 60ECh. P.4 - Prob. 61ECh. P.4 - Prob. 62ECh. P.4 - Prob. 63ECh. P.4 - Prob. 64ECh. P.4 - Prob. 65ECh. P.4 - Prob. 66ECh. P.4 - Prob. 67ECh. P.4 - Prob. 68ECh. P.4 - Prob. 69ECh. P.4 - EXPLORING CONCEPTS Restricted Domain Explain how...Ch. P.4 - Prob. 71ECh. P.4 - Prob. 72ECh. P.4 - Prob. 73ECh. P.4 - Prob. 74ECh. P.4 - Prob. 75ECh. P.4 - Prob. 76ECh. P.4 - Prob. 77ECh. P.4 - Prob. 78ECh. P.4 - Prob. 79ECh. P.4 - Prob. 80ECh. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Prob. 4RECh. P - Prob. 5RECh. P - Prob. 6RECh. P - Prob. 7RECh. P - Prob. 8RECh. P - Prob. 9RECh. P - Prob. 10RECh. P - Prob. 11RECh. P - Prob. 12RECh. P - Prob. 13RECh. P - Prob. 14RECh. P - Prob. 15RECh. P - Prob. 16RECh. P - Prob. 17RECh. P - Prob. 18RECh. P - Prob. 19RECh. P - Prob. 20RECh. P - Prob. 21RECh. P - Prob. 22RECh. P - Prob. 23RECh. P - Prob. 24RECh. P - Prob. 25RECh. P - Prob. 26RECh. P - Prob. 27RECh. P - Prob. 28RECh. P - Prob. 29RECh. P - Sketching a Line in the Plane In Exercises 27-30,...Ch. P - Prob. 31RECh. P - Prob. 32RECh. P - Finding Equations of Lines Find equations of the...Ch. P - Prob. 34RECh. P - Rate of Change The purchase price of a new machine...Ch. P - Break-Even Analysis A contractor purchases a piece...Ch. P - Prob. 37RECh. P - Prob. 38RECh. P - Evaluating a Function In Exercises 37-40, evaluate...Ch. P - Prob. 40RECh. P - Prob. 41RECh. P - Prob. 42RECh. P - Prob. 43RECh. P - Prob. 44RECh. P - Prob. 45RECh. P - Prob. 46RECh. P - Prob. 47RECh. P - Prob. 48RECh. P - Prob. 49RECh. P - Prob. 50RECh. P - Transformations of Functions Use a graphing...Ch. P - Think About It What is the minimum degree of the...Ch. P - Prob. 53RECh. P - Prob. 54RECh. P - Prob. 55RECh. P - Prob. 56RECh. P - Prob. 57RECh. P - Prob. 58RECh. P - Prob. 59RECh. P - Prob. 60RECh. P - Prob. 61RECh. P - Prob. 62RECh. P - Prob. 63RECh. P - Prob. 64RECh. P - Prob. 65RECh. P - Prob. 66RECh. P - Prob. 67RECh. P - Prob. 68RECh. P - Prob. 69RECh. P - Prob. 70RECh. P - Prob. 71RECh. P - Prob. 72RECh. P - Prob. 73RECh. P - Prob. 74RECh. P - Prob. 75RECh. P - Prob. 76RECh. P - Prob. 77RECh. P - Prob. 78RECh. P - Prob. 79RECh. P - Prob. 80RECh. P - Prob. 81RECh. P - Prob. 82RECh. P - Prob. 83RECh. P - Prob. 84RECh. P - Prob. 85RECh. P - Prob. 86RECh. P - Prob. 87RECh. P - Prob. 88RECh. P - Prob. 89RECh. P - Prob. 90RECh. P - Prob. 1PSCh. P - Finding Tangent Lines There are two tangent lines...Ch. P - Heaviside Function The Heaviside function H(x) is...Ch. P - Sketching Transformations Consider the graph of...Ch. P - Prob. 5PSCh. P - Prob. 6PSCh. P - Prob. 7PSCh. P - Prob. 8PSCh. P - Slope of a Tangent Line One of the fundamental...Ch. P - Slope of a Tangent Line Sketch the graph of the...Ch. P - Prob. 11PSCh. P - Graphing an Equation Explain how you would graph...Ch. P - Sound Intensity A large room contains two speakers...Ch. P - Sound Intensity Suppose the speakers in Exercise...Ch. P - Lemniscate Let d1 and d2 be the distances from the...
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