01 - CHAPTER 1 Preparation for Calculus Section 1.1 Section...

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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 Fitting Models to Data . . . . . . . . . . . . . . . . . . . . 32 Section 1.5 Inverse Functions . . . . . . . . . . . . . . . . . . . . . . 34 Section 1.6 Exponential and Logarithmic Functions . . . . . . . . . . . 50 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
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7. x 2 4 2 6 6 4 64 6 ( 3, 5) (3, 5) ( 2, 0) (0, 4) (2, 0) y y 5 4 2 x 2 8. 6 4 2 2 2 2 4 4 6 6 8 10 y x y 5 s x 2 3 d 2 x 02 3 y 040 2 5 2 5 2 2 2 3 CHAPTER 1 Preparation for Calculus Section 1.1 Graphs and Models 2 1. x -intercept: y -intercept: Matches graph (b). s 0, 2 d s 4, 0 d y 52 1 2 x 1 2 3. x -intercepts: y -intercept: Matches graph (a). s 0, 4 d s 2, 0 d , s 2 2, 0 d y 5 4 2 x 2 5. x 2 2 4 6 8 4 6 8 4 6 84 6 8 ( 4, 5) ( 2, 2) (0, 1) (2, 4) (4, 7) y y 5 3 2 x 1 1 x 024 y 147 2 2 2 5 2 2 2 4 2. x -intercepts: y -intercept: Matches graph (d). s 0, 3 d s 2 3, 0 d , s 3, 0 d y 5 ! 9 2 x 2 4. x -intercepts: y -intercept: Matches graph (c). s 0, 0 d s 0, 0 d , s 2 1, 0 d , s 1, 0 d y 5 x 3 2 x 6. 6 4 22 2 4 6 6 10 y x y 5 6 2 2 x x 0123 4 y 10 86420 2 2 2 1 2 2 x 0123456 y 9 4 10149
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Section 1.1 Graphs and Models 3 9. x 2 2 4 6 4 62 ( 3, 1) ( 1, 1) ( 4, 2) ( 2, 0) (0, 2) (1, 3) ( 5, 3) y y 5 | x 1 2 | 11. x 4 6 8 2 6 8 4 10 10 22 1 6 14 18 12 (0, 4) (1, 3) (4, 2) (16, 0) y (9, 1) y 5 ! x 2 4 x 01 y 3 2 101 2 3 2 1 2 2 2 3 2 4 2 5 x 0 149 1 6 y 0 2 1 2 2 2 3 2 4 10. 33 3 4 2 2 2 2 1 1 1 1 y x y 5 | x | 2 1 12. 55 1 0 15 20 2 3 4 5 y x y 5 ! x 1 2 x 0123 y 2 10 0 1 2 2 1 2 1 2 2 2 3 x 02 7 1 4 y 0 12 3 4 ! 2 2 1 2 2 16. Note that when or x 5 10. x 5 0 y 5 10 Xmin = -30 Xmax = 30 Xscl = 5 Ymin = -10 Ymax = 50 Yscl = 5 15. Note that when x 5 0. y 5 4 Xmin = -3 Xmax = 5 Xscl = 1 Ymin = -3 Ymax = 5 Yscl = 1 13. 1 2 123 1 1 2 3 x (1, 2) (2, 1) ( 2, 1) ( 1, 2) 3, ) 2 3 ) ) 2 3 3, y y 5 2 x 14. x 3, ) 1 4 1, ) 1 2 ) 1 4 5, ) 1 2 3, y 2345 3 4 2 3 4 (2, 1) (0, 1) 1 y 5 1 x 2 1 x 2 3 y Undef. 2 1 2 3 2 2 2 1 2 2 3 2 1 2 2 2 3 x 2 3 5 y Undef. 1 1 4 1 2 2 1 2 1 2 2 1 4 2 1 2 3
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4 Chapter 1 Preparation for Calculus 18. (a) (b) and s x , 2 4 d 5 s 1, 2 4 d s x , 2 4 d 5 s 2 1.65, 2 4 d s 2 0.5, y d 5 s 2 0.5, 2.47 d 9 6 9 6 y 5 x 5 2 5 x 17. (a) (b) s x , 3 d 5 s 2 4, 3 d s 3 5 ! 5 2 s 2 4 d d s 2, y d 5 s 2, 1.73 d s y 5 ! 5 2 2 5 ! 3 < 1.73 d 66 3 5 ( 4.00, 3) (2, 1.73) y 5 ! 5 2 x 19. y -intercept: x -intercepts: x 52 2, 1; s 2 2, 0 d , s 1, 0 d 0 5 s x 1 2 ds x 2 1 d 0 5 x 2 1 x 2 2 y 2; s 0, 2 2 d y 5 0 2 1 0 2 2 y 5 x 2 1 x 2 2 21. y -intercept: x -intercepts: x 5 0, ± 5; s 0, 0 d ; s ± 5, 0 d 0 5 x 2 ! s 5 2 x ds 5 1 x d 0 5 x 2 ! 25 2 x 2 y 5 0; s 0, 0 d y 5 0 2 ! 25 2 0 2 y 5 x 2 ! 25 2 x 2 20. y -intercept: x -intercepts: x 5 0, ± 2; s 0, 0 d , s ± 2, 0 d 0 5 x s x 2 2 ds x 1 2 d 0 5 x 3 2 4 x y 5 0; s 0, 0 d y 2 5 0 3 2 4 s 0 d y 2 5 x 3 2 4 x 22. y -intercept: x -intercept: x 5 1; s 1, 0 d 0 5 s x 2 1 d ! x 2 1 1 y 1; s 0, 2 1 d y 5 s 0 2 1 d ! 0
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This note was uploaded on 11/13/2010 for the course MATH MAT 231 taught by Professor Thurber during the Spring '08 term at Thomas Edison State.

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01 - CHAPTER 1 Preparation for Calculus Section 1.1 Section...

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