Name Algebra 2 & Trigonometry

Name Algebra 2 & Trigonometry Chapter 4 - Functions

1. Given f(x) = 2x2 + 3x – 9 and g(x) = 3x - 5, find: a. f(x) + g(x)

b. f(x) – g(x)

c. (f(x))(g(x))

d. f(g(x))

e. g(f(x))

2. Draw a mapping representing a function that is NOT one-to-one.

3. Find the domain of the following and state the domain using interval notation. a. f(x) = 3x

b. g(x) = 11 √2x – 7

c. h(x) = -6 x2 - 11x + 24

d. f(x) = √x + 2 - 9

4. Given f(x) = 2x + 3, g(x) = -x2 + 6x + 11, and h(x) =√3x + 16 , evaluate: a. h(4) leave your answer in simplest radical form b. f(g(2)) c. f-1(5) d. g(f(h(-4))) 5. a. Find the inverse of f(x) = 3x - 8 5 b. Using the composition of functions, prove that f(x) and f-1(x) are inverse functions.

6. Given the graphs provided, find: a. f( 3) b. g(f(-2)) c. find all values of x such that g(x) = 4 d. State the domain and range of f(x)

7. Find the range of the following functions: a. g (x) = √x + 3 b. f(x) = 2x2 + 12x + 7

c. y = |x| - 9

8. Given the function y = x2, write the equation that would represent the function after being altered by the following conditions: a. Shift the graph down 4 units b. Shift the graph to the left 3 units c. Flip the graph over the x-axis d. The vertex (turning point) is located at (5, 3) 9. Given f(x) = 6x2 – 17x – 10, find all values of x such that f(x) = 4.

10. State the coordinates of the turning point for the following transformations of the graph of y = |x|. a. y =|x| - 3 b. y = |x + 2| c. y = -|x| d. y = |x – 4| + 5

11. a. Draw a graph of an equation that represents a function. b. Draw a graph of an equation that does NOT represent a function.

12. State the domain and range of the function shown below.