Name___________________________________ Algebra II
Date______________ Review for Functions Quiz #2
Topics on the Quiz: One-to-One Functions
Inverses of Functions
Even and Odd Functions
Key Features of Functions
1. How can you tell if a function is one-to-one by looking at a set of points?
2. How can you tell if a function is one-to-one by looking at its graph?
3. If a function is one-to-one, what is true about its inverse?
4. How do you find the inverse of a function?
5. What symmetry does the graph of an even function have?
6. If a function is even, and f(2) = 3, what is the value of f(-2)?
7. What symmetry does the graph of an odd function have?
8. If a function is odd, and f(2) = 3, what is the value of f(-2)?

9. Given the graph of f(x) below, graph f -1 (x) on the same set of axes.
10. Given
( )
= x +
2
3 5
, find the equation of the inverse of f.
11. If f(x) is an even function, and f(1) = 9, what is the value of 10f(-1)?
12. Is the function
( )
= x + 3 even, odd or neither? Justify your answer.

13. Given the graph of f(x) to the right,
a. Evaluate f(0).
b. State the zeroes of f(x).
c. Over which of the following intervals is
f(x) always decreasing?
(1) 1 x < 4 (2) 3
(3) 1 x < 3
<
(4) 4 x x
< 6
< 4
d. What is the absolute maximum of the function?
e. State the intervals over which
( )
≤ 0 .
f. Is f(x) a one-to-one function? Why or why not?
14. If f(x) is a one-to-one function, and f(3) = -2, what point must be on the graph of
f -1 (x)?

Answers
1. All x-values are different and all y-values are different.
2. It passes the VLT.
3. The inverse will be a function.
4. Interchange the x and y.
5. y-axis
6. 3
7. origin
8. -3
9. graph
10. f − 1 ( )
= 2 x + 7
11. 90
12. Neither – the graph of f(x) does not have y-axis symmetry or origin symmetry
13. a. -3
b. -3, 1, 5, 7
c. (2)
d. (-4, 5) or just 5
e. 3 x ≤ 1 and 5 ≤ x ≤ 7
f. No, the graph doesn’t pass the HLT
14. (-2, 3)