400 CHAPTER 6 Algebra, Graphs, and Functions 4. The set of values obtained for the dependent variable is called the ________ of the function. Range 5. In a quadratic function of the form = + + f x ax bx c ( ) , 2 if a is greater than 0, then the graph of f x( ) is a parabola that opens________. Upward 6. In a quadratic function of the form = + + f x ax bx c ( ) , 2 if a is less than 0, then the graph of f x( ) is a parabola that opens ________. Downward 7. The formula used to determine the equation for the axis of symmetry of a parabola is ________. = − x b a2 8. A test that is used to determine whether a graph represents a function is called the ________ line test. Vertical In Exercises 9–16, determine whether the set of ordered pairs is a function. 9. { } − (2, 5), (4, 9), (1, 6), ( 1, 3) Yes 10. ( 4, 2), (1, 5), (3, 7), (5, 6) { } − − Yes 11. { } − (2, 5), (2, 7), (2, 1), (2, 2) No 12. { } − − − − ( 1, 2), ( 1, 4), ( 1, 6), ( 1, 9) No 13. { } − − − − ( 1, 1), (0, 1), (3, 1) Yes 14. { } (1,1), (2,1), (3,1), (4,1) Yes 15. { } (1, 1),(1, 2),(1, 3),(1, 4) No 16. { } − (4, 2), (4, 3), (4, 5) No Practice the Skills In Exercises 17–30, determine whether the graph represents a function. If it does represent a function, give its domain and range. 17. 2 22 22 2 y x Function, domain: = − − x 2, 1, 1, 2, 3; = − y range: 1, 1, 2, 3 18. 2 22 22 2 y x Not a function 19. 22 22 2 y x 2 Function, domain: R range: R 20. 2 22 22 2 y x Function, domain: R range: R 21. 2 22 22 2 y x Not a function 22. –2 –2 2 y x 2 Function, domain: R; range: = y 2 23. 6 26 26 6 y x Function, domain: R range: y 4 ≥ − 24. 15 215 215 15 y x Function, domain: R range: ≤ y 10 25. 22 2 y x 22 2 Not a function 26. 28 22 8 2 y x Function, domain: ≤ < x 0 12; range: = y 1, 2, 3 27. 230 230 30 30 y x Function, domain: ;R range: ;R 28. 24 –4 4 4 y x Function, domain: ;R range > y 0 29. 22 10 2 y x Function, domain: ≤ ≤ x 0 10; range: − ≤ ≤ y 1 3 30. 22 22 2 2 y x 23 3 23 3 Not a function In Exercises 31–40, evaluate the function for the given value of x. 31. = − + = − f x x x ( ) 3 3, 1 6 32. = + = − f x x x ( ) 8 2, 2 −14 33. = − + = f x x x x ( ) 3 1, 4 2 5 34. = − = f x x x ( ) 5, 7 2 44
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