3_2 - Chapter 3 Functions and Their Graphs 3.2 1. The Graph...

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Chapter 3 300 Functions and Their Graphs 3.2 The Graph of a Function 1. x 2 + 4 y 2 = 16 x -intercepts: x 2 + 4 0 ( 29 2 = 16 x 2 = 16 x = ± 4 ⇒ - 4,0 ( 29 , 4,0 ( 29 y -intercepts: 0 ( 29 2 + 4 y 2 = 16 4 y 2 = 16 y 2 = 4 y = ± 2 0, - 2 ( 29 , 0,2 ( 29 2. False 3. vertical 4. f 5 ( 29 = - 3 5. f x ( 29 = ax 2 + 4 a - 1 ( 29 2 + 4 = 2 a = - 2 6. False 7. False 8. True 9. (a) f (0) = 3 since (0,3) is on the graph. f ( - 6) = - 3 since ( - 6, - 3) is on the graph. (b) f (6) = 0 since (6,0) is on the graph. f (11) = 1 since (11,1) is on the graph. (c) f (3) is positive since f (3) 3.7. (d) f ( - 4) is negative since f ( - 4) ≈ - 1. (e) f ( x ) = 0 when x = - 3, x = 6, and x = 10. (f) f ( x ) 0 when - 3 < x < 6, and 10 < x 11. (g) The domain of f is x - 6 x 11 { } or - 6,11 [ ] (h) The range of f is y - 3 y 4 { } or - 3,4 [ ] (i) The x -intercepts are (–3, 0), (6, 0), and (11, 0). (j) The y -intercept is (0, 3) (k) The line y = 1 2 intersects the graph 3 times. (l) The line x = 5 intersects the graph 1 time (m) f ( x ) = 3 when x = 0 and x = 4. (n) f ( x ) = - 2 when x = - 5 and x = 8.
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Section 3.2 The Graph of a Function 301 10. (a) f (0) = 0 since (0,0) is on the graph. f (6) = 0 since (6,0) is on the graph. (b) f (2) = - 2 since (2, - 2) is on the graph. f ( - 2) = 1 since ( - 2,1) is on the graph. (c) f (3) is negative since f (3) ≈ - 1. (d) f ( - 1) is positive since f ( - 1) ≈ - 0.4. (e) f ( x ) = 0 when x = 0, x = 4, and x = 6. (f) f ( x ) < 0 when 0 < x < 4. (g) The domain of f is x - 4 x 6 { } or - 4,6 [ ] (h) The range of f is y - 2 y 3 { } or - 2, 3 [ ] (i) The x -intercepts are (0, 0), (4, 0), and (6, 0). (j) The y -intercept is (0, 0). (k) The line y =- 1 intersects the graph 2 times. (l) The line x = 1 intersects the graph 1 time. (m) f ( x ) = 3 when x = 5. (n) f ( x ) = - 2 when x = 2. 11. Not a function since vertical lines will intersect the graph in more than one point. 12. Function (a) Domain: x x is any real number { } ; Range: y y 0 { } (b) intercepts: (0,1) 13. Function (a) Domain: x -π≤ x ≤π { } ; Range: y - 1 y 1 { } (b) intercepts: - π 2 ,0 , π 2 ,0 , (0,1)
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3_2 - Chapter 3 Functions and Their Graphs 3.2 1. The Graph...

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