Practice for Function and Relations Unit Test
Algebra2/Trig
Name ________________________________
1. For each relation below determine a) its domain, b) its range, and c) whether the relation is a function.
a) {(1,3) (2,5) (6,9) (3,0) (4,1)}
.
b)
D: ____________________
R: ____________________
Function? _____________
.
c)
.
-1
0
1
2
0
1
4
D: ____________________
R: ____________________
Function? _____________
D: ____________________
R: ____________________
Function? _____________
d) Which of the above functions are one-to-one?
e) Which of the above functions are onto?
f) Which of the above functions have an inverse that is itself a function?
2. Look at the graph of the function f (x) and answer the
questions:
a)
Evaluate f (3)
f(x)
b)
Evaluate ( f  f )(0)
3
Find the inverse of each function below and then state whether its inverse is also a function:
f ( x)  3x  7
a) J  (2,5), (5,7), (6,7)
b)
1
J 
f 1 ( x) 
c)
graph the inverse of h(x):
h(x)
4 Suppose you have d dollars and you go to a gas station and buy a bag of chips for $1.99. You then spend
the rest of your money on gas. Let’s say that g (d ) is the number of gallons of gas you can buy with d
dollars. Here’s the function:
d  1.99
g (d ) 
2.67
a) Evaluate and interpret in words g ( 28.50) . Round answer to nearest tenth.
b) Calculate how much money you need to purchase the chips and exactly 15 gallons of gas.
(Use the function and show your work.)
c) Let’s say that the amount of money you have is a function of how many hours you worked this week.
The function that tells us how much money (d) you have for working t hours is: d (t )  12t . Write a
function that would tell us how many gallons of gas (g) you could buy if you work t hours. Hint: This
function is g (d (t ))
5 Given the following functions, answer the questions below:
3x  1
2
f ( x) 
h( x ) 
g ( x)  2 x  3
x5
x
j ( x) 
1
x2
3
a. Domain of f (x) :
b. Domain of g (x ) :
c. Evaluate f (4)
d. Evaluate ( f  g )( 23)
e. Evaluate h( g (n))
f. Find j 1 ( x)
6 Given the graph of f(x) below, sketch and label the graphs of each transformation below:
a)
1
f ( x)
2
b)  f (x)
f(x)
f(x)
c) f ( x  8)
d) f ( x)  6
f(x)
f(x)
7. Solve each equation or inequality below. For each solution, be clear on if the answer is an “and” or
an “or” statement. Also, for each inequality, graph the solution on a number line.
1
 2 x  1  5  9
3
x  11 < 12
2
4
.
1
( x  1)  6
2
5 x  1  25
8. At 9:00 AM, Christina began to add water to a swimming pool at the rate of 25 gallons per minute. When
she began, the pool contained 80 gallons of water. Christina stopped adding water to the pool at 4:00 PM.
Let g be the number of gallons of water in the pool and t be the number of minutes that have past since
9:00 AM.
a. Write an equation for g as a function of t.
b. What is the domain of the function?
c. What is the range of the function?
d. Is the function one-to-one?