- 6 2 Assess Your Understanding Are You Prepared Answers Are Given At The End Of These Exercises If You Get A Wrong An 1 (105.8 KiB) Viewed 16 times
6.2 Assess Your Understanding 'Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 1 1. Suppose f(x) = 4x 2. Find d ƒ ( x + ²) ( (pp. 207-209) 2. Where is the function f(x) = increasing? Where is it decreasing? (pp. 231-232) 3. What is the domain of f(x) = Concepts and Vocabulary 5. If x₁ and x₂ are any two different inputs of a function f. then fis one-to-one if 6. If every horizontal line intersects the graph of a function fat no more than one point, then fis a(n) function. 7. If fis a one-to-one function and f(3) = 8, then f¹ (8) = x + 5 x² + 3x18 8. If f is the inverse of a function f, then the graphs of f and fare symmetric with respect to the line 9. If the domain of a one-to-one function fis [4,00), then the range of its inverse function fis 10. True or False If f and g are inverse functions, then the domain of fis the same as the range of g. 15. Skill Building In Problems 13-20, determine whether the function is one-to-one. 13. Range $200 $300 Domain 20 Hours 25 Hours 30 Hours 40 Hours Domain 20 Hours 25 Hours 30 Hours 40 Hours (pp. 211-213) 17. {(2,6), (-3, 6), (4,9), (1, 10) } 19. {(0,0), (1, 1), (2, 16), (3, 81)} $350 $425 Range $200 $350 $425 22. SECTION 6.2 One-to-One Functions; Inverse Functions 431 4. Simplify: 14. 16. (c) 11. Multiple Choice If (-2,3) is a point on the graph of a one-to-one function f, which of the following points is on the graph of fl (a) (3,-2) (b) (2, -3) (c) (-3.2) (d) (-2,-3) 12. Multiple Choice Suppose f is a one-to-one function with a domain of [xx 3} and a range of Which of the following is the domain of f¹? (a) {x|x = 3} (b) All real numbers f x + Domain Bob Dave John Chuck X 1 x² Domain Bob Dave John Chuck +1 -1 (pp. 67-69) (d) 23. -3 18. (-2,5), (-1,3), (3, 7), (4, 12)} 20. {(1,2), (2,8), (3, 18), (4,32) } In Problems 21-26, the graph of a function fis given. Use the horizontal-line test to determine whether f is one-to-one. 21. 3 f f 3 X -3 3 + Range Range y Karla Debral Dawn Phoebe f Karla Debra Phoebe 3 x