Name
1.
2.
Algebra 2 & Trigonometry
Chapter 4 - Functions
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))
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.
a.
b.
c.
d.
Given the graphs provided, find:
f( 3)
g(f(-2))
find all values of x such that g(x) = 4
State the domain and range of f(x)
7.
a.
Find the range of the following functions:
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.