CHAPTER 1 Preparation for Calculus Section 1.1 Graphs and Models ................................................................................. 2 Section 1.2 Linear Models and Rates of Change ................................................... 11 Section 1.3 Functions and Their Graphs ................................................................. 22 Section 1.4 Review of Trigonometric Functions .................................................... 36 Section 1.5 Inverse Functions .................................................................................. 45 Section 1.6 Exponential and Logarithmic Functions ............................................. 62 Review Exercises .......................................................................................................... 72 Problem Solving ........................................................................................................... 87 2 © 2024 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. CHAPTER 1 Preparation for Calculus Section 1.1 Graphs and Models 1. To find the x-intercepts of the graph of an equation, let y be zero and solve the equation for x. To find the y-intercepts of the graph of an equation, let x be zero and solve the equation for y. 2. Symmetry helps in sketching a graph because you need only half as many points to plot. Answers will vary. 3. 3 2 y x =− + 3 x-intercept: ( ) 2, 0 y-intercept: ( ) 0, 3 Matches graph (b). 4. 2 y x = − 9 x-intercepts: ( )( ) −3, 0 , 3, 0 y-intercept: ( ) 0, 3 Matches graph (d). 5. 2 y x = − 3 x-intercepts: ( ) 3, 0 , 3, 0 ( ) − y-intercept: ( ) 0, 3 Matches graph (a). 6. 3 yx x = − x-intercepts: ( )( )( ) 0, 0 , 1, 0 , 1, 0 − y-intercept: ( ) 0, 0 Matches graph (c).