Unit 2 - Functions Exam 2020

Name: ____________________________________ Score: ________ / 32 UNIT #2 - FUNCTIONS Part I Questions  1. If g  x  x2  5 and h  x  7x 11, then which of the following is the value of g h 3 ? [2pts]  2. If f x represents a one-to-one function, which of the following could be the value of k?[2 pts] (1) 20 (3) 7 x 3 1 2 3 5 7 10 (2) 11 f  x 11 4 k 5 8 11 20 (4) 8 3. If f  x  5x  7 , then what is the solution to f  x  4 ?[2 pts] 4. Which of the following values of x does not lie in the domain of y  9  5x ?[2 pts] (1) 1 (3) 0 (2) 2 (4) 1 f 8  2 5. If f x is a one-to-one function and then which of the following points must lie on the graph  of its inverse, i.e. y  f 1 x ?[2 pts] (1) 8, 2 (3)  1 ,  1 (2) 2,  8  8 2  (4) 2, 8

6. The graph of f(x) pictured below and h(x) = 10 – x2 . Find h(f(0)). [4 pts] PART II QUESTIONS: Answer all questions in this part. Clearly indicate the necessary steps and explain your reasoning. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 7. Given the equation f (x)  3 x  6, state the equation for the inverse of f (x) in simplest mx+b form? [ 4pts] 2 8. Two functions are given below in table and equation form. Using these functions, give the value of g  f 1(1) . Show how you arrived at your answer. [4pts] x 4 1 0 3 7 10 g x  5x  2 f  x 8 6 1 5 2 4

x9 9. What value (s) of x would not be in the domain of the function g(x) = 2x  9 . [2 pts]    10. The function f x is shown graphed below. Create a graph of its inverse, f 1 x . [2 pts]  11. For the function f x = x2 + 1, a. find f-1 (x). [2 pts] b. Evaluate f-1 (17). [2 pts] c. Show how f(f-1(x)) = x. [2pts]