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

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C H A P T E R 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 P A R T I
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C H A P T E R P Preparation for Calculus Section P.1 Graphs and Models Solutions to Odd-Numbered Exercises 2 1. x -intercept: y -intercept: Matches graph (b) 0, 2 4, 0 y 1 2 x 2 3. x -intercepts: y -intercept: Matches graph (a) 0, 4 2, 0 , 2, 0 y 4 x 2 5. x 2 2 4 6 8 4 6 8 4 6 8 4 6 8 ( 4, 5) ( 2, 2) (0, 1) (2, 4) (4, 7) y y 3 2 x 1 7. x 2 4 2 6 6 4 6 4 6 ( 3, 5) (3, 5) ( 2, 0) (0, 4) (2, 0) y y 4 x 2 x 0 2 4 y 1 4 7 2 5 2 4 x 0 2 3 y 0 4 0 5 5 2 3 9. x 2 2 4 6 4 6 2 ( 3, 1) ( 1, 1) ( 4, 2) ( 2, 0) (0, 2) (1, 3) ( 5, 3) y y x 2 11. x 4 6 8 2 6 8 4 10 10 2 2 16 14 18 12 (0, 4) (1, 3) (4, 2) (16, 0) y (9, 1) y x 4 x 0 1 y 3 2 1 0 1 2 3 1 2 3 4 5 x 0 1 4 9 16 y 0 1 2 3 4
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Section P.1 Graphs and Models 3 13. Note that when x 0. y 4 Xmin = -3 Xmax = 5 Xscl = 1 Ymin = -3 Ymax = 5 Yscl = 1 15. (a) (b) x , 3 4, 3 3 5 4 2, y 2, 1.73 y 5 2 3 1.73 6 6 3 5 ( 4.00, 3) (2, 1.73) 17. y -intercept: x -intercepts: x 2, 1; 2, 0 , 1, 0 0 x 2 x 1 0 x 2 x 2 y 2; 0, 2 y 0 2 0 2 y x 2 x 2 19. y -intercept: x -intercepts: x 0, ± 5; 0, 0 ; ± 5, 0 0 x 2 5 x 5 x 0 x 2 25 x 2 y 0; 0, 0 y 0 2 25 0 2 y x 2 25 x 2 21. y -intercept: None. x cannot equal 0. x -intercepts: x 4; 4, 0 0 2 x 0 3 2 x x y 3 2 x x 23. y -intercept: x -intercept: x 0; 0, 0 x 2 0 x 2 4 0 0 y 0; 0, 0 0 2 y 0 2 4 y 0 x 2 y x 2 4 y 0 25. Symmetric with respect to the y -axis since y x 2 2 x 2 2. 27. Symmetric with respect to the x -axis since y 2 y 2 x 3 4 x . 29. Symmetric with respect to the origin since x y xy 4. 31. No symmetry with respect to either axis or the origin. y 4 x 3 33. Symmetric with respect to the origin since y x x 2 1 . y x x 2 1 35. is symmetric with respect to the y -axis since y x 3 x x 3 x x 3 x . y x 3 x 37. Intercepts: Symmetry: none 2 3 , 0 , 0, 2 0 y ) 2 0 ( , 2 1 x 3 2 1 1 , 2 3 y 3 x 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 8, 0 , 0, 4 y x 2 4 41. Intercepts: Symmetry: y -axis x ) 0 (1, 0, 1) y 2 ) , ( 1 0 ( 1 2 2 2 1, 0 , 1, 0 , 0, 1 y 1 x 2 43. Intercepts: Symmetry: none x 2 2 8 10 12 8 6 10 2 4 ( 3, 0) (0, 9) y 3, 0 , 0, 9 y x 3 2 45. Intercepts: Symmetry: none y 5 4 3 3 x 3 2 , 1 1 1 , 2 3 ) 0 2 ) (0 2 ( 3 2 , 0 , 0, 2 y x 3 2 47. Intercepts: Symmetry: none Domain: x 1 2 3 4 5 2 6 4 3 1 4 1 2 3 ( 2, 0) (0, 0) y x 2 0, 0 , 2, 0 y x x 2 49. Intercepts: Symmetry: origin x 1 2 3 4 2 3 4 2 1 3 4 2 3 4 (0, 0) y 0, 0 x y 3 51. Intercepts: none Symmetry: origin y 3 1 2 x 3 2 1 y 1 x 53. Intercepts: Symmetry: y -axis 0, 6 , 6, 0 , 6, 0 x 2 2 4 2 6 8 4 6 8 4 2 8 4 6 8 ( 6, 0) (0, 6) (6, 0) y y 6 x 55. Intercepts: Symmetry: x -axis 0, 3 , 0, 3 , 9, 0 1 4 11 4 ( 9, 0) (0, 3) (0, 3) y ± x 9 y 2 x 9 y 2 x 9 57.
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