College Algebra 7th Edition
ISBN: 9781305115545
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: James Stewart, Lothar Redlin, Saleem Watson
P Prerequisites 1 Equations And Graphs 2 Functions 3 Polynomial And Rational Functions 4 Exponential And Logarithmic Functions 5 Systems Of Equations And Inequalities 6 Matrices And Determinants 7 Conic Sections 8 Sequences And Series 9 Counting And Probability A Calculations And Significant Figures B Graphing With A Graphing Calculator Chapter2: Functions
2.1 Functions 2.2 Graphs Of Functions 2.3 Getting Information From The Graph Of A Function 2.4 Average Rate Of Change Of A Function 2.5 Linear Functions And Models 2.6 Transformations Of Functions 2.7 Combining Functions 2.8 one-to-one Functions And Their Inverses Chapter Questions Section: Chapter Questions
Problem 1CC Problem 2CC: Describe the four ways of representing a function. Problem 3CC: Sketch graphs of the following function by hand. (a) f(x)=x2 (b) g(x)=x3 (c) h(x)=|x| (d) k(x)=x Problem 4CC: What is a piecewise defined function? Give an example. Problem 5CC: (a) What is the Vertical Line Test, and what is it used for? (b) What is the Horizontal Line Test,... Problem 6CC: Define each concept,and give an example of each. (a) Increasing function (b) Decreasing function (c)... Problem 7CC: Suppose we know that the point (3,5) is a point on the graphof a function f . Explain how to find... Problem 8CC: What does it mean to say that f(4) is a local maximum valueof f ? Problem 9CC Problem 10CC Problem 11CC: Suppose the graph of a function f is given. Write an equation for each of the graphs that art... Problem 12CC Problem 13CC Problem 14CC Problem 15CC Problem 1E: Function NotationA verbal description of a function f is given. Find a formula that expresses f in... Problem 2E: Function NotationA verbal description of a function f is given. Find a formula that expresses f in... Problem 3E: Function in wordsAformula for a function f is given. Give a verbal description of the function.... Problem 4E: Function in words A formula for a function f is given. Give a verbal description of the function.... Problem 5E: Table of Values Complete the table of values for the given function. g(x)=x24x Problem 6E: Table of Values Complete the table of values for the given function. h(x)=3x2+2x5 Problem 7E: Printing Cost A publisher estimates that the cost C(x) of printing a run of x copies of a certain... Problem 8E: Earnings Reynalda works as a salesperson in the electronics division of a department store. She... Problem 9E: Evaluating FunctionsEvaluate the function at the indicated values. f(x)=x24x+6 ;... Problem 10E: Evaluating FunctionsEvaluate the function at the indicated values.... Problem 11E: Functions Given by a GraphWhich of the following figuresare graphof function? Which of the functions... Problem 12E: Getting Information from a Graph A graph of a function f is given. (a) Find f(2) and f(2) . (b) Find... Problem 13E: Domain and Range Find the domain and range of the function. f(x)=x+3 Problem 14E: Domain and Range Find the domain and range of the function. F(t)=t2+2t+5 Problem 15E: DomainFind the Domain of the function. f(x)=7x+15 Problem 16E: Domain Find the domain of the function. f(x)=2x+12x1 Problem 17E: Domain Find the Domain of the function. f(x)=x+4 Problem 18E: Domain Find the domain of the function. f(x)=3x2x+1 Problem 19E: Domain Find the domain of the function. f(x)=1x+1x+1+1x+2 Problem 20E: Domain Find the domain of the function. g(x)=2x2+5+32x253 Problem 21E: Domain Find the domain of the function. h(x)=4x+x21 Problem 22E: Domain Find the domain of the function. f(x)=2x+132x3+2 Problem 23E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 24E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 25E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 26E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 27E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 28E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 29E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 30E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 31E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 32E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 33E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 34E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 35E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 36E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 37E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 38E: Graphing Functions Sketch a graph of the function. Use transformations of function whenever... Problem 39E: Equations That Represent Functions Determine whether the equation defines y as a function of x .... Problem 40E: Equations That Represent Functions Determine whether the equation defines y as a function of x .... Problem 41E: Equations That Represent Functions Determine whether the equation defines y as a function of x .... Problem 42E: Equations That Represent Functions Determine whether the equation defines y as a function of x .... Problem 43E: Graphing Functions Determine which viewing rectangle produces the most appropriate graph of the... Problem 44E: Graphing Functions Determine which viewing rectangle produces the most appropriate graph of the... Problem 45E: Domain and Range from a Graph A function f is given. (a) Use a graphing calculator to draw the graph... Problem 46E: Domain and Range from a Graph A function f is given. (a) Use a graphing calculator to draw the graph... Problem 47E: Domain and Range from a Graph A function f is given. (a) Use a graphing calculator to draw the graph... Problem 48E: Domain and Range from a Graph A function f is given. (a) Use a graphing calculator to draw the graph... Problem 49E: Getting Information from a Graph Draw a graph of the function f , and determine the intervals on... Problem 50E: Getting Information from a Graph Draw a graph of the function f , and determine the intervals on... Problem 51E: Net Change and Average Rate of Change A function is given either numerically, graphically, or... Problem 52E: Net Change and Average Rate of Change A function is given either numerically, graphically, or... Problem 53E: Net change and average rate of change A function is given (either numerically, graphically, or... Problem 54E: Net Change and Average Rate of Change A function is given either numerically, graphically, or... Problem 55E: Net Change and Average Rate of Change A function is given either numerically, graphically, or... Problem 56E: Net Change and Average Rate of Change A function is given either numerically, graphically, or... Problem 57E: Linear? Determine whether the given function is linear. f(x)=(2+3x)2 Problem 58E: Linear? Determine whether the given function is linear. g(x)=x+35 Problem 59E: Linear Functions A linear functions is given. (a) Sketch a graph of the function. (b) What is the... Problem 60E: Linear Functions A linear functions is given. (a) Sketch a graph of the function. (b) What is the... Problem 61E: Linear Functions A linear functions is described either verbally, numerically, or graphically.... Problem 62E: Linear Functions A linear functions is described either verbally, numerically, or graphically.... Problem 63E: Linear Functions A linear functions is described either verbally, numerically, or graphically.... Problem 64E: Linear Functions A linear functions is described either verbally, numerically, or graphically.... Problem 65E: Linear Functions A linear functions is described either verbally, numerically, or graphically.... Problem 66E: Linear Functions A linear functions is described either verbally, numerically, or graphically.... Problem 67E: Population The population of a planned seaside community in Florida is given by the function... Problem 68E: Retirement Savings Ella is saving for her retirement by making regular deposits into a 401(k) plan.... Problem 69E: Average Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0... Problem 70E: Average Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0... Problem 71E: Transformations Suppose the graph of f is given. Describe how the graphs of the following functions... Problem 72E: Transformations The graph of f is given. Draw the graphs of the following functions. (a) y=f(x2) (b)... Problem 73E: Even and Odd Functions Determine whether f is even, odd, or neither. (a) f(x)=2x53x2+2 (b) f(x)=x3x7... Problem 74E: Even and Odd Functions Determine whether f is even, odd, or neither. Problem 75E: Local Maxima and Minima Find the local maximum and minimum values of the function and the due of x... Problem 76E: Local Maxima and Minima Find the local maximum and minimum values of the function and the due of x... Problem 77E: Local Maxima and Minima Find the local maximum and minimum values of the function and the due of x... Problem 78E: Local Maxima and Minima Find the local maximum and minimum values of the function and the due of x... Problem 79E: Maximum Height of Projectile A stone is thrown upward from the top of a building. Its height (in... Problem 80E: Maximum Profit The profit P (in dollars) generated by selling x units of a certain commodity ¡s... Problem 81E: Graphical Addition Two functions, f and g ,are given. Draw graphs of f , g , and f+g on the same... Problem 82E: Graphical Addition Two Functions, f and g ,are given. Draw graphs of f , g , and f+g on the same... Problem 83E: Combinig Functions If f(x)=x23x+2 and g(x)=43x ,find the following functions. (a) f+g (b) fg (c) fg... Problem 84E: If f(x)=1+x2 and g(x)=x1 ,find the following. (a) fg (b) gf (c) (fg)(2) (d) (ff)(2) (e) fgf (f) gfg Problem 85E: Composition of Functions Find the functions fg , gf , ff and gg and their domains.... Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E Problem 99E Problem 100E Problem 101E Problem 102E: Graphing Inverse Functionss (a)Show that the function f(x)=1+x4 is one-to-one. (b)Sketch the graph... Problem 1T: Which of the following are graphs of functions? If the graph is that of a function, is itone-to-one? Problem 2T Problem 3T: A function f has the following verbal description: “Subtract 2, then cube the result.” (a) Find a... Problem 4T Problem 5T Problem 6T Problem 7T Problem 8T Problem 9T Problem 10T Problem 11T Problem 12T Problem 13T Problem 14T Problem 15T Problem 16T Problem 17T: A graph of a function f is given below. Find f(0) and f(4) Problem 18T Problem 19T Problem 20T Problem 21T: A graph of a function f is given below. Sketch the graph of f1 . Problem 22T Problem 1P: In these problem you are asked to find a function that models a real-life situation. Use the... Problem 2P Problem 3P Problem 4P Problem 5P Problem 6P Problem 7P Problem 8P Problem 9P Problem 10P Problem 11P Problem 12P Problem 13P: In these problems you are asked to find a function that models a real-life situation. Use the... Problem 14P Problem 15P: In these problem you are asked to find a function that models a real-life situation. Use the... Problem 16P Problem 17P Problem 18P Problem 19P Problem 20P: In these problem you are asked to find a function that models a real-life situation and then use the... Problem 21P Problem 22P: In these problems you are asked to find a function that model a real-life situation and then use the... Problem 23P: In these problems you are asked to find a function that models a real-life situation and use the... Problem 24P: In these problems you are to find a function that models a real-life situation and then use the... Problem 25P Problem 26P Problem 27P Problem 28P Problem 29P: In these problems you are asked to find a function that models a real-life situation and then use... Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the... Problem 31P: In this problem you are asked to find a function that models in real life situation and then use the... Problem 32P Problem 8CC: What does it mean to say that f(4) is a local maximum valueof f ?
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Concept explainers
Explain the difference between an absolute maximum and a local maximum . Illustrate with a sketch.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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