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Name ___________________ Date ________________ Pre -Calculus Function Unit Review 1. Refer to the graph on the right to answer the following questions a. Is this a graph of a function? _________ b. What is the Domain? ________________ c. What is the Rang e? _________________ d. What are the zeros? _________________ 2. Give the Domain and zeros of each of the following a. b. D = ______________ D = _________________ Z’s ______________ Z’s _________________ 3. Use the graph of f(x) and g(x) to find each of the following a. f(2) – g(2) ____________________ b. f(x) – g(x) positive_______________ c. f(x) – g(x) negative_______________ d. f(x) – g(x) zero _________________ d. f(4) + g( -3) __________________ 2 y x 5     2 f x x 4  1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 x 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 y f(x) g(x) 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 x 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 y 4. Let and , find each of the following a. b. c. d. e. f. g. If find 5. Given the graph of a. Does f(x) have an inverse? _________ b. Explain   2 f x x 2x 3      g x x 3     f g x    f g 3   f x g       f g x     g f x     g f 4   h x x 1        g h f 5   fx 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 x 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 y 6. If and , show that f and g are inverses of each other. 7. Suppose f(x) has an inverse, if f(1) = 0 and f(2) = -1 find each of the following a. b. c. 10. State whether the function f has an inverse. If exits, find it. a. b. Does the inverse exists _____ Does the inverse exists _____ = _____________ = __________ __ c. d. Does the inverse exists _____ Does the inverse exists _____ = _____________ = _____________   x3 fx 4     g x 4x 3    1 f1      1 f f 2     1 f f 1 1 f   f x x 2    1 fx 2x  1 f 1 f   f x 2x 3, x 0      f x x 1 , x 0, y 0     1 f 1 f

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