3_4 - Chapter 3 Functions and Their Graphs 3.4 1. Library...

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Chapter 3 320 Functions and Their Graphs 3.4 Library of Functions; Piecewise-Defined Functions 1. y = x 2. y = 1 x 3. y = x 3 - 8 y - intercept : Let x = 0, then y = 0 ( 29 3 - 8 = - 8 (0, - 8) x - intercept : Let y = 0, then 0 = x 3 - 8 x 3 = 8 x = 2 (2,0) 4. less 5. piecewise-defined 6. True 7. False 8. False 9. C 10. A 11. E 12. G 13. B 14. D 15. F 16. H
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Section 3.4 Library of Functions; Piecewise-Defined Functions 321 17. f x ( 29 = x 18. f x ( 29 = x 2 19. f x ( 29 = x 3 20. f x ( 29 = x 21. f x ( 29 = 1 x 22. f x ( 29 = x
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Chapter 3 Functions and Their Graphs 322 23. f ( x ) = x 3 24. f x ( 29 = 3 25. (a) f ( - 2) = ( - 2) 2 = 4 (b) f (0) = 2 (c) f (2) = 2(2) + 1 = 5 26. (a) f ( - 1) = ( - 1) 3 = - 1 (b) f (0) = 3(0) + 2 = 2 (c) f (1) = 3(1) + 2 = 5 27. (a) f (1.2) = int(2(1.2)) = int(2.4) = 2 (b) f (1.6) = int(2(1.6)) = int(3.2) = 3 (c) f ( - 1.8) = int(2( - 1.8)) = int( - 3.6) = - 4 28. (a) f (1.2) = int 1.2 2  = int(0.6) = 0 (b) f (1.6) = int 1.6 2  = int(0.8) = 0 (c) f ( - 1.8) = int - 1.8 2  = int( - 0.9) = - 1 29. f ( x ) = 2 x if x 0 1 if x = 0 (a) Domain: x x is any real number { } (b) x- intercept: none y- intercept: (0,1) (c) (d) Range: y y 0 { } 30. f ( x ) = 3 x if x 0 4 if x = 0 (a) Domain: x x is any real number { } (b) x- intercept: none y- intercept: (0, 4) (c) (d) Range: y y 0 { }
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Section 3.4 Library of Functions; Piecewise-Defined Functions 323 31. f ( x ) = - 2 x + 3 if x < 1 3 x - 2 if x 1 (a) Domain: x x is any real number { } (b) x- intercept: none y- intercept: (0,3) (c) (d) Range: y y 1 { } 32. f ( x ) = x + 3 if x < - 2 - 2 x - 3 if x ≥ - 2 (a) Domain: x x is any real number { } (b) x- intercepts: (–3, 0), (–1.5, 0) y- intercept: (0, –3) (c) (d) Range: y y 1 { } 33. f ( x ) = x + 3 if - 2 x < 1 5 if x = 1 - x + 2 if x 1 (a) Domain: x x ≥ - 2 { } (b) x- intercept: (2, 0) y- intercept: (0, 3) (c) (d) Range: y y < 4 { } and y = 5 34. f ( x ) = 2 x + 5 if - 3 x < 0 - 3 if x = 0 - 5 x if x 0 (a) Domain: x x ≥ - 3 { } (b) x- intercept: (–2.5, 0) y- intercept: (0, –3) (c) (d) Range: y y < 5 { }
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Chapter 3 Functions and Their Graphs 324 35. f ( x ) = 1 + x if x < 0 x 2 if x 0 (a) Domain: x x is any real number { } (b) x- intercepts: (–1,0), (0,0) y- intercept: (0,0) (c) (d) Range: y y is any real number { } 36. f ( x ) = 1 x if x < 0 x 3 if x 0 (a) Domain: x x is any real number { } (b) x- intercept: (0,0) y- intercept: (0,0) (c)
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3_4 - Chapter 3 Functions and Their Graphs 3.4 1. Library...

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