ODD0P - PART I CHAPTER P Preparation for Calculus Section...

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CHAPTER P Preparation for Calculus Section P.1 Graphs and Models . . . . . . . . . . . . . . . . . . . . . . 2 Section P.2 Linear Models and Rates of Change . . . . . . . . . . . . . 7 Section P.3 Functions and Their Graphs . . . . . . . . . . . . . . . . . 14 Section P.4 Fitting Models to Data . . . . . . . . . . . . . . . . . . . . 18 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 PART I
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CHAPTER P Preparation for Calculus Section P.1 Graphs and Models Solutions to Odd-Numbered Exercises 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 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 x 024 y 147 2 2 2 5 2 2 2 4 x 02 3 y 040 2 5 2 5 2 2 2 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 2101 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
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Section P.1 Graphs and Models 3 13. Note that when x 5 0. y 5 4 Xmin = -3 Xmax = 5 Xscl = 1 Ymin = -3 Ymax = 5 Yscl = 1 15. (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) 17. 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 19. 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 21. y -intercept: None. x cannot equal 0. x -intercepts: x 5 4; s 4, 0 d 0 5 2 2 ! x 0 5 3 s 2 2 ! x d x y 5 3 s 2 2 ! x d x 23. y -intercept: x -intercept: x 5 0; s 0, 0 d x 2 s 0 d 2 x 2 1 4 s 0 d 5 0 y 5 0; s 0, 0 d 0 2 s y d 2 0 2 1 4 y 5 0 x 2 y 2 x 2 1 4 y 5 0 25. Symmetric with respect to the y -axis since y 5 s 2 x d 2 2 2 5 x 2 2 2. 27. Symmetric with respect to the x -axis since s 2 y d 2 5 y 2 5 x 3 2 4 x . 29. Symmetric with respect to the origin since s 2 x ds 2 y d 5 xy 5 4. 31. No symmetry with respect to either axis or the origin. y 5 4 2 ! x 1 3 33. Symmetric with respect to the origin since y 5 x x 2 1 1 . 2 y 5 2 x s 2 x d 2 1 1 35. is symmetric with respect to the y -axis since y 5 | s 2 x d 3 1 s 2 x d | 5 | 2 s x 3 1 x d | 5 | x 3 1 x | . y 5 | x 3 1 x | 37. Intercepts: Symmetry: none s 2 3 , 0 d , s 0, 2 d 0 y ) 2 0 (, 2 1 x 3 2 1 1 , 2 3 y 3 x 1 2
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4 Chapter P Preparation for Calculus 39. Intercepts: Symmetry: none x 10 8 ) 0 , 8 ( y 4 2 ) 4 , 2 ( 2 0 2 8 6 10 s 8, 0 d , s 0, 2 4 d y 5 x 2 2 4 41. Intercepts: Symmetry: y -axis x ) 0 (1, 0, 1) y 2 ) , ( 10 ( 1 2 2 2 s 1, 0 d , s 2 1, 0 d , s 0, 1 d y 5 1 2 x 2 43. Intercepts: Symmetry: none x 2 2 8 10 12 8 6 10 2 4 ( 3, 0) (0, 9) y s 2 3, 0 d , s 0, 9 d y 5 s x 1 3 d 2 45. Intercepts: Symmetry: none y 5 4 3 3 x 3 2 , 1 1 1 , 2 3 ) 0 2 ) (0 2 ( s 2 3 ! 2 , 0 d , s 0, 2 d y 5 x 3 1 2 47. Intercepts: Symmetry: none Domain: x 1 2 3 4 5 2 6 4 3 14 123 ( 2, 0) (0, 0) y x 2 2 s 0, 0 d , s 2 2, 0 d y 5 x !
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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ODD0P - PART I CHAPTER P Preparation for Calculus Section...

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