3_3 - Chapter 3 Functions and Their Graphs 3.3 1. 2. 3....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 3 308 Functions and Their Graphs 3.3 Properties of Functions 1. 2 x 5 2. slope = y x = 8 - 3 3 - - 2 ( 29 = 5 5 = 1 3. y = 2 x 2 + 3 Test for symmetry: x - axis: Replace y by - y : - y = 2 x 2 + 3 y = - 2 x 2 - 3, which is not equivalent to y = 2 x 2 + 3. y Replace x by - x y = 2 - x ( 29 2 + 3 = 2 x 2 + 3, which equivalent to y = 2 x 2 + 3. Origin: Replace x by - x and y by - y - y = 2 - x ( 29 2 + 3 y = - 2 x 2 - 3, which is not equivalent to y = 2 x 2 + 3. Therefore, the graph is symmetric with respect to the y -axis. 4. y - y 1 = m x - x 1 ( 29 y - - 2 ( 29 = 5 x - 3 ( 29 y + 2 = 5 x - 3 ( 29 5. y = x 2 - 9 y - intercept : Let x = 0, then y = 0 2 - 9 = - 9 (0, - 9) x - intercepts: Let y = 0, then 0 = x 2 - 9 x 2 = 9 x = ± 3 ( - 3,0), 3,0 ( 29 6. increasing 7. even, odd 8. True 9. True 10. False 11. Yes 12. No, it is increasing. 13. No, it only increases on (5, 10). 14. Yes 15. f is increasing on the intervals - 8, - 2 ( 29 , 0,2 ( 29 , 5, ( 29 . 16. f is decreasing on the intervals: -∞ , - 8 ( 29 , - 2,0 ( 29 , 2,5 ( 29 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Section 3.3 Properties of Functions 309 17. Yes. The local maximum at x = 2 is 10. 18. No. There is a local minimum at x = 5. 19. f has local maxima at x = - 2 and x = 2. The local maxima are 6 and 10, respectively. 20. f has local minima at x = - 8, x = 0 and x = 5. The local minima are –4, 0, and 0, respectively. 21. (a) Intercepts: (–2,0), (2,0), and (0,3). (b) Domain: x - 4 x 4 { } ; Range: y 0 y 3 { } . (c) Increasing: (–2, 0) and (2, 4); Decreasing: (–4, –2) and (0, 2). (d) Since the graph is symmetric with respect to the y -axis, the function is even. 22. (a) Intercepts: (–1, 0), (1, 0), and (0, 2). (b) Domain: x - 3 x 3 { } ; Range: y 0 y 3 { } . (c) Increasing: (–1, 0) and (1, 3); Decreasing: (–3, –1) and (0, 1). (d) Since the graph is symmetric with respect to the y -axis, the function is even. 23. (a) Intercepts: (0,1). (b) Domain: x x is any real number { } ; Range: y y > 0 { } . (c) Increasing: ( -∞ , ) ; Decreasing: never. (d) Since the graph is not symmetric with respect to the y -axis or the origin, the function is neither even nor odd. 24. (a) Intercepts: (1, 0). (b) Domain: x x > 0 { } ; Range: y y is any real number { } . (c) Interval notation: Increasing: (0, ) ; Decreasing: never. (d) Since the graph is not symmetric with respect to the y -axis or the origin, the function is neither even nor odd. 25. (a) Intercepts: ( ,0),( π ,0), and (0,0) . (b) Domain: x -π≤ x ≤π { } ; Range: y - 1 y 1 { } . (c) Increasing: - π 2 , π 2 ; Decreasing: , - π 2 and π 2 , π . (d) Since the graph is symmetric with respect to the origin, the function is odd. 26. (a) Intercepts: - π 2 , 0 , π 2 , 0 , and (0, 1). (b) Domain: x x ; Range: y - 1 y 1 { } . (c) Increasing: ,0 ( 29 ; Decreasing: 0, π ( 29 . (d) Since the graph is symmetric with respect to the y -axis, the function is even.
Background image of page 2
Chapter 3 Functions and Their Graphs 310 27. (a) Intercepts: 1 2 ,0 , 5 2 , and 0, 1 2 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

Page1 / 12

3_3 - Chapter 3 Functions and Their Graphs 3.3 1. 2. 3....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online