3_1 - Chapter 3 284 Functions and Their Graphs 3.1...

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Unformatted text preview: Chapter 3 284 Functions and Their Graphs 3.1 Functions 1. (1,3) 2. 3 2 ( 29 2- 5 2 ( 29 + 1 2 = 12- 10 + 1 2 = 5 2 3. We must not allow the denominator to be 0. x + 4 x - 4 ; Domain: x x - 4 { } . 4. 3- 2 x 5 5. independent, dependent- 2 x 2 x < - 1 6. range 7. The intersection of the intervals [0,7] and [2,5], i.e., [0,5]. 8. does not equal, f , g 9. g- f ( 29 x ( 29 10. False 11. True 12. True 13. True 14. False 15. Function Domain: {Dad, Colleen, Kaleigh, Marissa} Range: {Jan. 8, Mar. 15, Sept. 17} 16. Function Domain: {Bob, Dave, John, Chuck} Range: {Beth, Diane, Linda, Marcia} 17. Not a function 18. Function Domain: {Bob, Dave, John, Chuck} Range: {Diane, Linda, Marcia} 19. Not a function 20. Function Domain: {2, 1, 3, 4} Range: {3, 5, 7, 12} 21. Function Domain: {1, 2, 3, 4} Range: {3} 22. Function Domain: {0, 1, 2, 3} Range: {2, 3, 7} Section 3.1 Functions 285 23. Not a function 24. Not a function 25. Function Domain: {2, 1, 0, 1} Range: {4, 1, 0} 26. Function Domain: {2, 1, 0, 1} Range: {3, 4, 16} 27. f x ( 29 = 3 x 2 + 2 x- 4 (a) f ( 29 = 3 0 ( 29 2 + 2 0 ( 29- 4 = - 4 (b) f 1 ( 29 = 3 1 ( 29 2 + 2 1 ( 29- 4 = 3 + 2- 4 = 1 (c) f- 1 ( 29 = 3- 1 ( 29 2 + 2- 1 ( 29- 4 = 3- 2- 4 = - 3 (d) f- x ( 29 = 3- x ( 29 2 + 2- x ( 29- 4 = 3 x 2- 2 x- 4 (e)- f x ( 29 = - 3 x 2 + 2 x- 4 ( 29 = - 3 x 2- 2 x + 4 (f) f x + 1 ( 29 = 3 x + 1 ( 29 2 + 2 x + 1 ( 29- 4 = 3 x 2 + 2 x + 1 ( 29 + 2 x + 2- 4 = 3 x 2 + 6 x + 3 + 2 x + 2- 4 = 3 x 2 + 8 x + 1 (g) f 2 x ( 29 = 3 2 x ( 29 2 + 2 2 x ( 29- 4 = 12 x 2 + 4 x- 4 (h) f x + h ( 29 = 3 x + h ( 29 2 + 2 x + h ( 29- 4 = 3 x 2 + 2 xh + h 2 ( 29 + 2 x + 2 h- 4 = 3 x 2 + 6 xh + 3 h 2 + 2 x + 2 h- 4 28. f x ( 29 = - 2 x 2 + x- 1 (a) f ( 29 = - 2 0 ( 29 2 +- 1 = - 1 (b) f 1 ( 29 = - 2 1 ( 29 2 + 1- 1 = - 2 (c) f- 1 ( 29 = - 2- 1 ( 29 2 +- 1 ( 29- 1 = - 4 (d) f- x ( 29 = - 2- x ( 29 2 +- x ( 29- 1 = - 2 x 2- x- 1 (e)- f x ( 29 = -- 2 x 2 + x- 1 ( 29 = 2 x 2- x + 1 (f) f x + 1 ( 29 = - 2 x + 1 ( 29 2 + x + 1 ( 29- 1 = - 2 x 2 + 2 x + 1 ( 29 + x + 1- 1 = - 2 x 2- 4 x- 2 + x = - 2 x 2- 3 x- 2 (g) f 2 x ( 29 = - 2 2 x ( 29 2 + 2 x ( 29- 1 = - 8 x 2 + 2 x- 1 (h) f x + h ( 29 = - 2( x + h ) 2 + x + h ( 29- 1 = - 2 x 2 + 2 xh + h 2 ( 29 + x + h- 1 = - 2 x 2- 4 xh- 2 h 2 + x + h- 1 Chapter 3 Functions and Their Graphs 286 29. f x ( 29 = x x 2 + 1 (a) f ( 29 = 2 + 1 = 1 = (b) f 1 ( 29 = 1 1 2 + 1 = 1 2 (c) f- 1 ( 29 =- 1- 1 ( 29 2 + 1 =- 1 1 + 1 = - 1 2 (d) f- x ( 29 =- x- x ( 29 2 + 1 =- x x 2 + 1 (e)- f x ( 29 = - x x 2 + 1 =- x x 2 + 1 (f) f x + 1 ( 29 = x + 1 x + 1 ( 29 2 + 1 = x + 1 x 2 + 2 x + 1 + 1 = x + 1 x 2 + 2 x + 2 (g) f 2 x ( 29 = 2 x 2 x ( 29 2 + 1 = 2 x 4 x 2 + 1 (h) f x + h ( 29 = x + h x + h ( 29 2 + 1 = x + h x 2 + 2 xh + h 2 + 1 30. f x ( 29 = x 2- 1 x + 4 (a) f ( 29 = 2- 1 + 4 =- 1 4 = - 1 4 (b) f 1 ( 29 = 1 2- 1 1 + 4 = 5 = (c) f- 1 ( 29 =- 1 ( 29 2- 1- 1 + 4 = 3 = (d) f- x ( 29 =- x ( 29 2- 1- x + 4 = x 2- 1- x + 4 (e)- f x ( 29 = - x 2...
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This homework help was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

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3_1 - Chapter 3 284 Functions and Their Graphs 3.1...

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