# EVEN0P - PART II CHAPTER P Preparation for Calculus Section...

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CHAPTER P Preparation for Calculus Section P.1 Graphs and Models . . . . . . . . . . . . . . . . . . . . . 282 Section P.2 Linear Models and Rates of Change . . . . . . . . . . . . 287 Section P.3 Functions and Their Graphs . . . . . . . . . . . . . . . . 292 Section P.4 Fitting Models to Data . . . . . . . . . . . . . . . . . . . 296 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 PART II

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CHAPTER P Preparation for Calculus Section P.1 Graphs and Models Solutions to Even-Numbered Exercises 282 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 8. 6 4 2 2 2 2 4 4 6 6 8 10 y x y 5 s x 2 3 d 2 x 0123 4 y 10 86420 2 2 2 1 2 2 x 0123456 y 9 410149 10. 33 3 4 2 2 2 2 1 1 1 1 y x y 5 | x | 2 1 12. 5 5 10 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
Section P.1 Graphs and Models 283 14. Note that when or x 5 10. x 5 0 y 5 10 Xmin = -30 Xmax = 30 Xscl = 5 Ymin = -10 Ymax = 40 Yscl = 5 16. (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 18. 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 20. y -intercept: x -intercepts: x 5 1; s 1, 0 d 0 5 s x 2 1 d ! x 2 1 1 y 52 1; s 0, 2 1 d y 5 s 0 2 1 d ! 0 2 1 1 y 5 s x 2 1 d ! x 2 1 1 22. y -intercept: x -intercepts: x 5 0, 2 3; s 0, 0 d , s 2 3, 0 d 0 5 x s x 1 3 d s 3 x 1 1 d 2 0 5 x 2 1 3 x s 3 x 1 1 d 2 y 5 0; s 0, 0 d y 5 0 2 1 3 s 0 d f 3 s 0 d 1 1 g 2 y 5 x 2 1 3 x s 3 x 1 1 d 2 24. y -intercept: x -intercepts: Note: is an extraneous solution. x ! 3 y 3 x 5 ! 3 3 ; 1 ! 3 3 , 0 ± x 5 ± ! 3 3 x 2 5 1 3 3 x 2 5 1 4 x 2 5 x 2 1 1 2 x 5 ! x 2 1 1 0 5 2 x 2 ! x 2 1 1 y 1; s 0, 2 1 d y 5 2 s 0 d 2 ! 0 2 1 1 y 5 2 x 2 ! x 2 1 1 26. No symmetry with respect to either axis or the origin. y 5 x 2 2 x 28. Symmetric with respect to the origin since y 5 x 3 1 x . 2 y x 3 2 x s 2 y d 5 s 2 x d 3 1 s 2 x d 30. Symmetric with respect to the x -axis since x s 2 y d 2 5 xy 2 10. 32. Symmetric with respect to the origin since xy 2 ! 4 2 x 2 5 0. s 2 x ds 2 y d 2 ! 4 2 s 2 x d 2 5 0

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284 Chapter P Preparation for Calculus 34. is symmetric with respect to the y -axis since y 5 s 2 x d 2 s 2 x d 2 1 1 5 x 2 x 2 1 1 . y 5 x 2 x 2 1 1 36. is symmetric with respect to the x -axis since | y | 2 x 5 3. | 2 y | 2 x 5 3 | y | 2 x 5 3 38. Intercepts: Symmetry: none 1 2 3 4 1 2 1 3 (4, 0) (0, 2) y x s 4, 0 d , s 0, 2 d y 52 x 2 1 2 40. Intercepts: Symmetry: none 1 1 12 2 2 y x 3 2 , 0 () (0, 1) s 0, 1 d , s 2 3 2 , 0 d y 5 2 3 x 1 1 42. Intercept: Symmetry: y -axis 3 6 3 6 9 12 (0, 3) y x s 0, 3 d y 5 x 2 1 3 44. Intercepts: Symmetry: none 1 2 3 1 2 3 1 3 5 2 4 (0, 0) 1 2 , 0 y x s 0, 0 d , s 2 1 2 , 0 d y 5 2 x 2 1 x 5 x s 2 x 1 1 d 46. Intercepts: Symmetry: origin 3 3 1 1 2 13 3 ( 2, 0) (2, 0) (0, 0) y x s 0, 0 d , s 2, 0 d , s 2 2, 0 d y 5 x 3 2 4 x 48.
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EVEN0P - PART II CHAPTER P Preparation for Calculus Section...

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