Name:
Period:
MU
College Algebra: CH#3 Polynomial and Rational Functions
You must show ALL your work for full credit. Calculators are not permitted on this test.
In problems 1 - 4, choose the one alternative that best completes the statement or answers the question.
Supporting work/reasoning MUST be shown in order to receive credit for your answer.
1. A polynomial function which could have the graph shown.
A.
f ( x )  ( x  1 )( x  2 )( x  1 )
B.
1
f ( x )   ( x  1 )( x  2 )( x  1 ) 2
2
C.
f ( x )  ( x  1 )( x  2 )( x  1 ) 2
1. ______
1
D. f ( x )    ( x  1)( x  2)( x  1) 2
 2
E. None of the above
2. A rational function which could have the graph shown.
A.
B.
C.
2. ______
x2  4
f(x)
x
2x 2  1
f(x)
x
x4
f(x)
x
D. f ( x ) 
x2  4
x2
E. None of the above
3. If the voltage in an electric circuit is kept at the same level, the current varies inversely with the resistance.
The current measures 40 amps when the resistance is 270 ohms. Determine the current when the resistance
is decreased to 100 ohms.
3. ______
A. 685 amps
B. 108 amps
C. 14.8 amps
D. 10.8 amps
E. None of the above
4. Solve in the complex number system.
1 



2i , 1  2i
B. 1  2i , 1  2i
C. 2i ,  2i
A.
2x 2  4x  10
4. ______
D. 1  2 , 1  2
E. None of the above
5. Determine the asymptotes of the rational function
A. V: x = 1 O: y  x  8
B. V: x = 2 H: y  1
2
C. V: x = 2 No horizontal or oblique
D. V: x = 1 O: y  1 x  4
2
E. None of the above
x 2  9x  5
2x  2
5. ______
Determine ALL complex zeros of the given polynomial functions. No decimal answers will be accepted.
4
2
6. h ( x )  3x  6x  189
7. f ( x)  x 3  8
6. _______________________ (+5)
7. _______________________ (+5)
Sketch the graph of the given polynomial function. Your sketch must include the coordinates of the zeros,
y-intercept, at least 1 additional point AND you must label all points with their respective coordinates in order
to receive full credit. Choose additional points to most accurately display the true shape of the graph. (+5)
8. f ( x )  ( x  1) ( x  3) ( x  1)
2
2
Solve the following inequalities algebraically. Show ALL supporting work for full credit. No decimal answers.
9. 2 x 2  7 x  15  0
10.
4x  1
2
3x  2
9. _____________________ (+5)
10. ____________________ (+5)
Sketch the graph of the rational function. Your sketch must include all zeros, intercepts, asymptotes (dotted
lines), and any points where asymptotes are crossed. You must label all points and all asymptotes with their
respective coordinates/equations in order to receive full credit. (+10)
11. f ( x ) 
x 3  2x 2
x2  9
Use the given zero to find the remaining zeros of the given function. State ALL complex zeros. No decimals.
12. h ( x )  x  8x  38x  58x  37 x  50;
5
4
3
2
zero : 3  4i
12. __________________________ (+5)
Determine ALL complex zeros of the polynomial f(x). Show ALL work/process for full credit. No decimals.
13. f ( x )  x  7 x  22 x  70 x  120
4
3
2
13. ___________________________ (+5)