Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 1 Homework, Page 102 Use a grapher to find all local maxima and minima and the values of x where they occur. Give values rounded to two decimal places. 41.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 2 Homework, Page 102 Use a grapher to find all local maxima and minima and the values of x where they occur. Give values rounded to two decimal places. 45.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 3 Homework, Page 102 State whether the function is even, odd, or neither. Support graphically and algebraically 49.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 4 Homework, Page 102 State whether the function is even, odd, or neither. Support graphically and algebraically 53.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 5 Homework, Page 102 Use a method of your choice to find all horizontal and vertical asymptotes. 57.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 6 Homework, Page 102 Use a method of your choice to find all horizontal and vertical asymptotes. 61.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 7 Homework, Page 102 Match the function with the graph by considering end behavior and asymptotes. 65.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 8 Homework, Page Graph the function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 9 Homework, Page a. The graph of this function does not intersect its vertical asymptote. Explain why not. The vertical asymptote is at the value of x where there is division by zero. Since division by zero is not defined, there is not a corresponding y-value.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page b. Show how you can add a single point to the graph of f and get a graph that does intersect its vertical asymptote.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page c. Is the graph in (b) the graph of a function. Yes, the graph in (b) is the graph of a piece-wise function.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Sketch a graph of a function f with domain all real numbers that satisfies all of the following: a. f is continuous for all x. b. f is increasing on (-∞, 0] and on [3, 5]. c. f is decreasing on [0, 3] and [5, ∞] d. f(0) = f(5) = 2 e. f(3) = 0
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page A function that is bounded above has an infinite number of upper bounds, but there is always a least upper bound. This least upper bound may or may not be in the range of f. For each of the following functions, find the upper bound and state whether or not it is in the range of the function. a. upper bound is y = 2 and it is in the range of the function.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page b. upper bound is y = 3 and it is not in the range of the function. c. upper bound is y = ∞ and it is not in the range of the function. d. upper bound is y = 2 and it is in the range of the function.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page e. upper bound is y = 1 and it is in the range of the function.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.3 Twelve Basic Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about What Graphs Can Tell You Twelve Basic Functions Analyzing Functions Graphically … and why As you continue to study mathematics, you will find that the twelve basic functions presented here will come up again and again. By knowing their basic properties, you will recognize them when you see them.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Identity Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Squaring Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Cubing Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Reciprocal Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Square Root Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Exponential Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Natural Logarithm Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Sine Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Cosine Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Absolute Value Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Greatest Integer Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Logistic Function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Looking for Domains One of the functions has domain the set of all reals except 0. Which function is it?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Analyzing a Function Graphically
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Analyzing a Function Graphically
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Analyzing a Function Graphically
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Analyzing a Function Graphically
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Review Section 1.3 Page 113, Exercises: (EOO), 59, 63
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.4 Building Functions from Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Combining Functions Algebraically Composition of Functions Relations and Implicitly Defined Functions … and why Most of the functions that you will encounter in calculus and in real life can be created by combining or modifying other functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Sum, Difference, Product, and Quotient
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Defining New Functions Algebraically
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Defining New Functions Algebraically
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Composition of Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Composition of Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Composing Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Composing Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Decomposing Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Decomposing Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Using Implicitly Defined Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Using Implicitly Defined Functions