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Name: ____________________________________ Period: ______ Date: _____________Table #: _____PRACTICE
ALGEBRA 2 HONORS: CHAPTER 9 EXAM
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find any points of discontinuity for the rational function.
x1
y  2
x  2x  8
A
B
____
B
C
D
D
x = 4, x = 2
x=1
(x  2)(x  5)
(x  5)(x  3)
asymptote: x = –3 and hole: x = –5
asymptotes: x = –3 and x = –5
asymptote: x = –2 and hole: x = –3
asymptote: x = 3 and hole: x = 5
3. Find the horizontal asymptote of the graph of y 
3x 2  6x  6
7x 2  x  6
.
3
C no horizontal asymptote
7
B
y=0
D y=1
4. Simplify the rational expression. State any restrictions on the variable.
y 2  9y  14
A
____
C
2. Describe the vertical asymptote(s) and hole(s) for the graph of y 
A
____
x = –4, x = 2
x = 4, x = –2
y=
y7
A
B
y  2; y  7
y  2; y  7
C
D
1
y  2; y  7
y  2; y  7
.
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
____
5. Simplify the rational expression. State any restrictions on the variable.
x 4  3x 2  10
x 4  7x 2  10
x2  5
A
B
____
x2  5
x2  5
x2  5
(x 2  5)
; x  2, x  5
;x  
2, x  
C
5
D
6. Sketch the asymptotes and graph the function.
2x  5
y 
x2
A
C
B
D
2
; x   2, x  
x2  5
x2  5
; x  2, x  5
x2  5
5
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
____
7. Multiply or divide. State any restrictions on the variables.
2c 4
7d 3

9d 2
5c 3
18c
A
B
____
35d
, c  0, d  0
18 7 5
c d , c  0, d  0
35
18c 7
C
D
8. Sketch the asymptotes and graph the function.
x 2  8x  15
y 
x 2  16
A
C
B
D
3
35d 5
35d
18c
, c  0, d  0
, c  0, d  0
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
____
9. Multiply or divide. State any restrictions on the variables.
d2
d6

d 2  8d  12
d2
A
d2
d2
d 2  2d
, d  6, 0,  2
d 2  2d
C
d2
d 2  2d
, d  6,  2
, d  6,  2
D
, d  6, 0,  2
d2
d2
____ 10. Multiply or divide. State any restrictions on the variables.
a6
a2
 2
a  3 a  8a  15
B
(a  6)(a  2)
A
, a  3, 5,  2
(a  3) 2 (a  5)
(a  6)(a  5)
, a  5,  2
B
a2
____ 11. Add or subtract. Simplify if possible.
6
1
 2
t  7 t  49
A
B
7
(t  7)(t  7)
6t  43
(t  7)(t  7)
(a  6)(a  2)
C
D
C
D
4
, a  3, 5
(a  3) 2 (a  5)
(a  6)(a  5)
, a  3,  2
a2
6t  41
(t  7)(t  7)
7
t 2  t  56
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
____ 12. Add or subtract. Simplify if possible.
p 2  11p  28
p 2  4p  21

6
p3
p4
A
C
p3
p 2  11p  22
p  10
B
p  10
D
p3
p 2  4p  21
____ 13. Add or subtract. Simplify if possible.
x 2  7x  10
x 2  4x  5
 2
x2  x  2
x  9x  20
2x 2  11x  5
A
x 2  7x  21
C
2x 2  10x  18
2x 2  7x  21
B
(x  1)(x  4)
2x 2  11x  5
D
(x  1)(x  4)
(x  1)(x  4)
____ 14. Simplify the complex fraction.
4
3

2a
3a
1
1

4a
a
A
4
5
B
2
C
1
2
d3
____ 15.
d 2  d  20
d7
d4
d3
A
B
(d  7)(d  5)
(d  3)(d  7)
(d  4)(d  5)
(d  3)(d  7)
C
D
5
(d  4) 2 (d  5)
(d  3)(d  5)
(d  7)(d  5)
D
5
4
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
____ 16. Solve the equation. Check the solution.
1
5

x1
x2
1
B 7
2
____ 17. Solve the equation. Check the solution.
a
2
1


a 2  36 a  6
a6
A

–9
B –6
____ 18. Solve the equation. Check the solution.
6
1

 1
2
x 9 x3
A
A
4
B
2
C

C
5
6
7
6
D

–9 and –6
D
6
C
1  73
2
D
3 or –4
C

D

____ 19. Solve the equation. Check the solution.
1
5

 5
6y 2y
A

4
15
B
8
3
Short Answer
20. Simplify the expression.
(t 4  1)(t 2  9)(t  9) 2
(t 4  81)(t 2  1)(t  1) 2
6
8
15
3
20
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
21. Simplify
7m2  28n 2
28n 2  7m2
22. Simplify.
x 2  x  xy  y
x 2  6x  7
x 2  2xy  y 2

4x  4y
23. Graph the function. Label any aystmptotes, holes, or discontinuities.
x3
f  x  2
x  5x  6
24. Graph the function. Label any aystmptotes, holes, or discontinuities.
9x 2  4
f x   2
3x  10x  8
7
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
25. Graph the function. Label any aystmptotes, holes, or discontinuities.
f  x 
x2  4
x2
p(x)
where q(x)  0. How do you determine if the function has a horizontal asymptote? a
q(x)
vertical asymptote? a hole?
26. Given f(x) 
27. Simplify.
xy  ay
1

ay  3a  2xy  6x a 2  4x 2
 1  2


 y  3 


8
ID: A
ALGEBRA 2 HONORS: CHAPTER 9 EXAM
Answer Section
MULTIPLE CHOICE
1. ANS:
REF:
OBJ:
KEY:
2. ANS:
REF:
OBJ:
KEY:
3. ANS:
REF:
OBJ:
KEY:
4. ANS:
OBJ:
TOP:
KEY:
5. ANS:
OBJ:
TOP:
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6. ANS:
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7. ANS:
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8. ANS:
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TOP:
9. ANS:
OBJ:
TOP:
KEY:
10. ANS:
OBJ:
TOP:
B
PTS: 1
DIF: L2
9-3 Rational Functions and Their Graphs
9-3.1 Properties of Rational Functions
TOP: 9-3 Example 1
rational function | point of discontinuity
A
PTS: 1
DIF: L2
9-3 Rational Functions and Their Graphs
9-3.1 Properties of Rational Functions
TOP: 9-3 Example 2
asymptote | vertical asympotote | rational function | graphing | hole in the graph of a function
A
PTS: 1
DIF: L2
9-3 Rational Functions and Their Graphs
9-3.1 Properties of Rational Functions
TOP: 9-3 Example 3
asymptote | graphing | rational function | horizontal asymptote
A
PTS: 1
DIF: L2
REF: 9-4 Rational Expressions
9-4.1 Simplifying Rational Expressions
STA: CA A2 7.0
9-4 Example 1
rational expression | simplifying a rational expression | restrictions on a variable
B
PTS: 1
DIF: L3
REF: 9-4 Rational Expressions
9-4.1 Simplifying Rational Expressions
STA: CA A2 7.0
9-4 Example 1
rational expression | simplifying a rational expression | restrictions on a variable
C
PTS: 1
DIF: L2
9-3 Rational Functions and Their Graphs
OBJ: 9-3.2 Graphing Rational Functions
9-3 Example 4
KEY: graphing | rational function
A
PTS: 1
DIF: L2
REF: 9-4 Rational Expressions
9-4.2 Multiplying and Dividing Rational Expressions
STA: CA A2 7.0
9-4 Example 3
simplifying a rational expression | restrictions on a variable | multiplying rational expressions
A
PTS: 1
DIF: L3
9-3 Rational Functions and Their Graphs
OBJ: 9-3.2 Graphing Rational Functions
9-3 Example 4
KEY: graphing | rational function
D
PTS: 1
DIF: L2
REF: 9-4 Rational Expressions
9-4.2 Multiplying and Dividing Rational Expressions
STA: CA A2 7.0
9-4 Example 3
simplifying a rational expression | restrictions on a variable | multiplying rational expressions
D
PTS: 1
DIF: L2
REF: 9-4 Rational Expressions
9-4.2 Multiplying and Dividing Rational Expressions
STA: CA A2 7.0
9-4 Example 4
KEY: restrictions on a variable | dividing rational expressions
1
ID: A
11. ANS:
REF:
OBJ:
TOP:
KEY:
12. ANS:
REF:
OBJ:
TOP:
KEY:
13. ANS:
REF:
OBJ:
TOP:
KEY:
14. ANS:
REF:
OBJ:
TOP:
KEY:
15. ANS:
REF:
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TOP:
KEY:
16. ANS:
OBJ:
KEY:
17. ANS:
OBJ:
KEY:
18. ANS:
OBJ:
KEY:
19. ANS:
OBJ:
KEY:
B
PTS: 1
DIF: L2
9-5 Adding and Subtracting Rational Expressions
9-5.1 Adding and Subtracting Rational Expressions
STA: CA A2 7.0
9-5 Example 3
simplifying a rational expression | adding rational expressions
B
PTS: 1
DIF: L2
9-5 Adding and Subtracting Rational Expressions
9-5.1 Adding and Subtracting Rational Expressions
STA: CA A2 7.0
9-5 Example 4
simplifying a rational expression | subtracting rational expressions
B
PTS: 1
DIF: L3
9-5 Adding and Subtracting Rational Expressions
9-5.1 Adding and Subtracting Rational Expressions
STA: CA A2 7.0
9-5 Example 3
simplifying a rational expression | adding rational expressions
A
PTS: 1
DIF: L2
9-5 Adding and Subtracting Rational Expressions
9-5.2 Simplifying Complex Fractions
STA:
CA A2 7.0
9-5 Example 5
complex fraction | simplifying a rational expression | simplifying a complex fraction
A
PTS: 1
DIF: L2
9-5 Adding and Subtracting Rational Expressions
9-5.2 Simplifying Complex Fractions
STA:
CA A2 7.0
9-5 Example 5
dividing rational expressions | simplifying a complex fraction
D
PTS: 1
DIF: L2
REF: 9-6 Solving Rational Equations
9-6.1 Solving Rational Equations
STA: CA A2 7.0
TOP: 9-6 Example 1
rational equation
A
PTS: 1
DIF: L2
REF: 9-6 Solving Rational Equations
9-6.1 Solving Rational Equations
STA: CA A2 7.0
TOP: 9-6 Example 2
rational equation | no solutions
A
PTS: 1
DIF: L2
REF: 9-6 Solving Rational Equations
9-6.1 Solving Rational Equations
STA: CA A2 7.0
TOP: 9-6 Example 2
rational equation | no solutions
C
PTS: 1
DIF: L2
REF: 9-6 Solving Rational Equations
9-6.1 Solving Rational Equations
STA: CA A2 7.0
TOP: 9-6 Example 2
rational equation
SHORT ANSWER
20. ANS:
(t  1)(t  9) 2
(t 2  9)(t  1)
PTS: 1
2
ID: A
21. ANS:
-1
PTS: 1
22. ANS:
4
xy
PTS: 1
23. ANS:
PTS: 1
DIF: Level B
REF: MAL21191
TOP: Lesson 8.3 Graph General Rational Functions
KEY: graph | rational function
MSC: Comprehension
NOT: 978-0-618-65615-8
24. ANS:
PTS: 1
DIF: Level B
REF: MAL21191
TOP: Lesson 8.3 Graph General Rational Functions
KEY: graph | rational function
MSC: Comprehension
NOT: 978-0-618-65615-8
3
ID: A
25. ANS:
PTS: 1
DIF: Level B
REF: MAL21191
TOP: Lesson 8.3 Graph General Rational Functions
KEY: graph | rational function
MSC: Comprehension
NOT: 978-0-618-65615-8
26. ANS:
see notes
PTS: 1
27. ANS:
3(a  xy  2x)
(y  3) 2 (a  2x)(a  2x)
PTS: 1
4
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