108 CHAPTER 2 Functions and Their Graphs ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 2.4 Assess Your Understanding 1. Graph y x. = (pp. 24–25) 2. Graph y x 1 . = (pp. 25–26) 3. Find the intercepts of the equation y x 8. 3 = − (p. 21) Concepts and Vocabulary 4. The function f x x2 ( ) = is decreasing on the interval . 5. When functions are defined by more than one equation, they are called functions. 6. True or False The cube function is odd and is increasing on the interval , . ( ) −∞ ∞ 7. True or False The cube root function is odd and is decreasing on the interval , . ( ) −∞ ∞ 8. True or False The domain and the range of the reciprocal function are the set of all real numbers. 9. Multiple Choice Which of the following functions has a graph that is symmetric about the y- axis? (a) y x = (b) y x = (c) y x3 = (d) y x 1 = 10. Multiple Choice Consider the following function. ( ) = − < + ≤ < ≥ ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ f x x x x x x 3 2 if 2 5 if 2 10 3 if 10 2 Which expression(s) should be used to find the y -intercept? (a) x3 2 − (b) x 5 2 + (c) 3 (d) all three Skill Building In Problems 11–18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function 11. 12. 13. 14. 15. 16. 17. 18. In Problems 19–26, graph each function. Be sure to label three points on the graph. 19. f x x ( ) = 20. f x x2 ( ) = 21. f x x3 ( ) = 22. f x x ( ) = 23. f x x 1 ( ) = 24. f x x ( ) = 25. f x x 3 ( ) = 26. f x 3 ( ) = 27. If ( ) = − < = − > ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ f x x x x x x if 0 4 if 0 find: 3 2 if 0 2 (a) f 3 ( ) − (b) f 0( ) (c) f 3( ) 28. If ( ) = − <− = − + >− ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ f x x x x x x 3 if 1 0 if 1 find: 2 1 if 1 2 (a) f 2 ( ) − (b) f 1 ( ) − (c) f 0( ) 29. If ( ) = + − ≤ ≤ − < ≤ ⎧ ⎨ ⎪ ⎩⎪⎪ f x x x x x 2 4 if 3 1 1 if 1 5 find: 3 (a) f 2 ( ) − (b) f 0( ) (c) f 1( ) (d) f 3( ) 30. If ( ) = − ≤ < + ≤ ≤ ⎧ ⎨ ⎪ ⎩⎪⎪ f x x x x x if 2 1 3 2 if 1 4 find: 3 (a) f 1 ( ) − (b) f 0( ) (c) f 1( ) (d) f 3( ) 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure In Problems 31 – 42 : (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. 31. ( ) = ≠ = ⎧ ⎨ ⎪ ⎩⎪⎪ f x x x x 2 if 0 1 if 0 32. ( ) = ≠ = ⎧ ⎨ ⎪ ⎩⎪⎪ f x x x x 3 if 0 4 if 0 33. ( ) = − + < − ≥ ⎧ ⎨ ⎪⎪ ⎩⎪⎪ f x x x x x 2 3 if 1 3 2 if 1
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