Pre-Calculus, Unit 3, Rational Functions
Test
Name: _________________________
Date: ____________
1. Graph the function. Label all asymptotes. State the
domain and range. (6 points)
f ( x) 
6 x
2x 1
Domain: ________________
Range: ________________
For 2 – 4, give the vertical, horizontal, and oblique
asymptotes. If there is no asymptote, write “NONE.”
4
2. y  2
x 2
(6 points each)
2. VA: ________________
HA: ________________
OA: ________________
3.
y
x2  4
x 2  8 x  15
3. VA: ________________
HA: ________________
OA: ________________
4.
4. VA: ________________
HA: ________________
OA: ________________
Perform the indicated operation and simplify. (4 points each)
5. 3x 2 y 6 y 2
6.

4 x3 y 5 2 xy 3
5. ________________
6. ________________
7.
x
6
 2
x  5 x  x  20
8.
3x
x3
 2
x  2 x  4 x  12
7. ________________
8. ________________
Simplify. (4 points each)
9.
2x
x3
x5
4 x  12
10.
x5
10 x 2
3 3

5 x
9. ________________
 15 x  16

x
4
11. _______________
10. _______________
Solve. (5 points each)
11.
8
5

x3 x3
12.
12. _______________
13.
2x
1
x3
14.
13. _______________
14. _______________
15. You have subscribed to a cable television service. The cable company
charges you a one-time installation fee of $30 and a monthly fee of $50.
Write and graph a model that gives the average cost per month as a function
of the number of months you have subscribed to the service. After how
many months will the average cost be $53? (10 points)
Equation:
_______________
Number of months:
_______________
16. What function
is graphed? (4
points)
20
A. y 
10 x  119
x  12
B. y 
10 x  121
x  12
C. y 
10 x  119
x  12
D. y 
10 x  121
x  12
18
16
14
12
10
8
6
4
E. None of these
2
5
17. What are all the solutions of the equation
10
15
20
6
x
 ? (4 points)
x7 2
A. -4
B. -3
C. -4, -3
D. -3, 4
E. 3, 4
18. If
, find
On the same grid, graph
(6 points)
and
Domain:
Range:
Domain:
Range:
19. Write the partial fraction decomposition for:
3x
. (8 points)
x 4
2