82 CHAPTER 2 Functions and Their Graphs Skill Building 11. Use the given graph of the function f to answer parts (a)–(n). x y 5 4 –3 –5 (2, 4) (6, 0) (0, 3) (4, 3) (8, –2) (–3, 0) (–5, –2) (–6, –3) 11 (10, 0) (11, 1) (a) Find f 0( ) and f 6 . ( ) − (b) Find f 6( ) and f 11 . ( ) (c) Is f 3( ) positive or negative? (d) Is f 4 ( ) − positive or negative? (e) For what values of x is f x 0? ( ) = (f) For what values of x is f x 0? ( ) > (g) What is the domain of f ? (h) What is the range of f ? (i) What are the x-intercepts? (j) What is the y-intercept? (k) How often does the line y 1 2 = intersect the graph? (l) How often does the line x 5 = intersect the graph? (m) For what values of x does f x 3? ( ) = (n) For what values of x does f x 2? ( ) = − 12. Use the given graph of the function f to answer parts (a)–(n). x y 2 4 6 4 2 –2 –4 –2 (6, 0) (5, 3) (0, 0) (4, 0) (2, –2) (–4, 2) (–2, 1) (a) Find f 0( ) and f 6 . ( ) (b) Find f 2( ) and f 2 . ( ) − (c) Is f 3( ) positive or negative? (d) Is f 1 ( ) − positive or negative? (e) For what values of x is f x 0? ( ) = (f) For what values of x is f x 0? ( ) < (g) What is the domain of f ? (h) What is the range of f ? (i) What are the x-intercepts? (j) What is the y-intercept? (k) How often does the line y 1 = − intersect the graph? (l) How often does the line x 1 = intersect the graph? (m) For what value of x does f x 3? ( ) = (n) For what value of x does f x 2? ( ) = − In Problems 13–24, determine whether or not the graph is that of a function by using the vertical-line test. In either case, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, the y-axis, or the origin 13. x y 3 3 23 23 14. x y 3 3 23 23 15. p 1 21 2p p–– 2 2 p–– 2 x y 16. 2 p–– 2 p p–– 2 2p x y 1 21 17. x y 3 3 23 23 18. x y 3 3 23 23 19. x y 3 3 23 23 (3, 2) 20. (4, 3) x y 4 4 24 24 21. (21, 2) (1, 2) x y 3 3 23 23 22. x y 3 3 23 23 23. x y 9 23 21 3 (2, 23) 6 3 24. x y 4 3 23 ( ) , 5 1 – 2
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