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Lesson 2 Quiz C Name______________________ 1. The graph of a function y = f(x) is given. Match each rule with the correct graph. i. g(x) = –f(x) ii) h(x) = f(x) – 2 Rule: Rule: Rule: Rule: iii) k(x) = f(x – 2) iv) p(x) = 2 – f(x) 2. The graph of y = x2 is translated so that the minimum is located at (5, -10). Write a function rule for the translated graph. Explain your reasoning. 3. The graph below gives the average high temperature in Albuquerque, New Mexico, as a function of the day of the year. Each day, the average low temperature in Albuquerque is approximately 45˚F lower than the average high temperature. a. What translation of the average high temperature graph will produce the graph of the average low temperature? b. Write a coordinate rule for the transformation you described in Part a. c. On the graph above, sketch the graph of the average low temperature in Albuquerque as a function of the day of the year. d. The function rule for the average high temperature graph is h(x) = 23 sin (0.17x – 2) + 70. Write a function rule for the average low temperature graph. Explain your reasoning 4. Consider a function f(x). The zeroes of the function are x = 3 and x = –2 and the y-intercept of the function is (0, –6). a. If possible, find the zeroes of g(x) = f(x + 5). If not possible explain why not. b. If possible, find the y-intercept of h(x) = –f(x). If not possible, explain why not. 5. Suppose that f(x) and g(x) are functions for which g(x) = f(x) + 5. a. If f(x) has a y-intercept of (0, 2), what (if anything) can be said about the y-intercept of g(x)? b. If f(x) has an x-intercept of (6, 0), what (if anything) can be said about the x-intercept of g(x)? a. f(x) = 5x - 6, transformation (x, y) →(x, -y + 7) b. f(x) = |𝑥|, transformation (x, y) →(x - 4, -2 - y) c. f(x) = x2 - 6x, transformation (x, y) →(x + 5, y - 8)