College Algebra
PRACTICE MILESTONE 5
Are you ready to take the Milestone 5?
Taking this practice test is a stress-free way to find out if you are ready for the Milestone 5 assessment. You can print it
out and test yourself to discover your strengths and weaknesses. The answer key is at the end of this Practice Milestone.
QUESTION 1
Suppose f (x) = 5 − x 2 and g (x) = 2x .
Perform the indicated operation on the functions and select the correct value.
Items to answer:
f (1) A. 1
1. g(2)
g(1) B. 2
2. f (2)
3. f (1)g(1) C. 4
4. f (2)g(2) D. 8
QUESTION 2
Suppose f (x) = 3x 2 + 1 and g (x) = 2x − 4 .
Find the value of f (g(1)) .
A. 5
B. 10
C. 13
D. 11
© 2016 Sophia Learning, LLC
, College Algebra
PRACTICE MILESTONE 5
QUESTION 3
Consider the function f (x) = √x + 4 .
Find the formula for the inverse function.
−1
A. f (x) = x 2 + 2
−1
B. f (x) = x − 2
−1
C. f (x) = x 2 + 4
−1
D. f (x) = x 2 − 4
QUESTION 4
Simplify the equation by canceling common factors:
x 2 −x−6
x 2 −6x−16
A. x−8
x−3
B. x−3
x−8
C. x−3
x+2
D. x+2
x−8
QUESTION 5
Write the following as a single rational expression.
1 1
x
+ 2−x
A. 2
x(2−x)
B. −2
x(2−x)
C. 1
2
D. 1
© 2016 Sophia Learning, LLC
, College Algebra
PRACTICE MILESTONE 5
QUESTION 6
Write the following as a single rational expression.
1 5
÷
x3 x2
A. 5x 2
B. 5x
C. 1
5x
D. 1
5x 2
QUESTION 7
Consider the function y = √3x − 12 .
What are the domain and range of this function?
A. Domain: x ≤ 4 , range: y ≥0
B. Domain: x ≥ 4 , range: y ≥0
C. Domain: x ≥ 0 , range: y ≥4
D. Domain: x ≤ 0 , range: y ≥4
QUESTION 8
Find the solution for x in the following equation.
2 4x = 32 x−1
A. x=5
B. x=7
C. x=3
D. x=4
© 2016 Sophia Learning, LLC
, College Algebra
PRACTICE MILESTONE 5
QUESTION 9
Match each function with its graph.
1. y = 2 • 3x
2. y =− 2 • 3x
3. y = 2 • 3−x
4. y =− 2 • 3−x
© 2016 Sophia Learning, LLC
PRACTICE MILESTONE 5
Are you ready to take the Milestone 5?
Taking this practice test is a stress-free way to find out if you are ready for the Milestone 5 assessment. You can print it
out and test yourself to discover your strengths and weaknesses. The answer key is at the end of this Practice Milestone.
QUESTION 1
Suppose f (x) = 5 − x 2 and g (x) = 2x .
Perform the indicated operation on the functions and select the correct value.
Items to answer:
f (1) A. 1
1. g(2)
g(1) B. 2
2. f (2)
3. f (1)g(1) C. 4
4. f (2)g(2) D. 8
QUESTION 2
Suppose f (x) = 3x 2 + 1 and g (x) = 2x − 4 .
Find the value of f (g(1)) .
A. 5
B. 10
C. 13
D. 11
© 2016 Sophia Learning, LLC
, College Algebra
PRACTICE MILESTONE 5
QUESTION 3
Consider the function f (x) = √x + 4 .
Find the formula for the inverse function.
−1
A. f (x) = x 2 + 2
−1
B. f (x) = x − 2
−1
C. f (x) = x 2 + 4
−1
D. f (x) = x 2 − 4
QUESTION 4
Simplify the equation by canceling common factors:
x 2 −x−6
x 2 −6x−16
A. x−8
x−3
B. x−3
x−8
C. x−3
x+2
D. x+2
x−8
QUESTION 5
Write the following as a single rational expression.
1 1
x
+ 2−x
A. 2
x(2−x)
B. −2
x(2−x)
C. 1
2
D. 1
© 2016 Sophia Learning, LLC
, College Algebra
PRACTICE MILESTONE 5
QUESTION 6
Write the following as a single rational expression.
1 5
÷
x3 x2
A. 5x 2
B. 5x
C. 1
5x
D. 1
5x 2
QUESTION 7
Consider the function y = √3x − 12 .
What are the domain and range of this function?
A. Domain: x ≤ 4 , range: y ≥0
B. Domain: x ≥ 4 , range: y ≥0
C. Domain: x ≥ 0 , range: y ≥4
D. Domain: x ≤ 0 , range: y ≥4
QUESTION 8
Find the solution for x in the following equation.
2 4x = 32 x−1
A. x=5
B. x=7
C. x=3
D. x=4
© 2016 Sophia Learning, LLC
, College Algebra
PRACTICE MILESTONE 5
QUESTION 9
Match each function with its graph.
1. y = 2 • 3x
2. y =− 2 • 3x
3. y = 2 • 3−x
4. y =− 2 • 3−x
© 2016 Sophia Learning, LLC
