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 x = –4, x = 2 C x = 4, x = 2
B x = 4, x = –2 D x=1
(x  2)(x  5)
____ 2. Describe the vertical asymptote(s) and hole(s) for the graph of y  .
(x  5)(x  3)

A asymptote: x = –3 and hole: x = –5

B asymptotes: x = –3 and x = –5
C asymptote: x = –2 and hole: x = –3
D asymptote: x = 3 and hole: x = 5
3x 2  6x  6
____ 3. Find the horizontal asymptote of the graph of y  .
7x 2  x  6

3
A y= 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
y7

A y  2; y  7 C y  2; y  7
B y  2; y  7 D y  2; y  7

1
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

____ 5. Simplify the rational expression. State any restrictions on the variable.
x 4  3x 2  10
x 4  7x 2  10

x2  5 (x 2  5)
A ; x  2, x  5 C ; x   2, x   5
x2  5 x2  5
x2  5 x2  5
B ;x   2, x   5 D ; x  2, x  5
x2  5 x2  5

____ 6. Sketch the asymptotes and graph the function.

2x  5
y 
x2
A C

B D

2
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

____ 7. Multiply or divide. State any restrictions on the variables.

2c 4 9d 2

7d 3 5c 3

18c 18c 7
A , c  0, d  0 C , c  0, d  0
35d 35d 5
18 7 5 35d
B c d , c  0, d  0 D , c  0, d  0
35 18c
____ 8. Sketch the asymptotes and graph the function.
x 2  8x  15
y 
x 2  16
A C

B D

3
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

____ 9. Multiply or divide. State any restrictions on the variables.

d2 d 2  8d  12

d6 d 2  2d

d2 d 2  2d
A , d  6, 0,  2 C , d  6,  2
d2 d2
d2 d 2  2d
B , 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

(a  6)(a  2) (a  6)(a  2)
A , a  3, 5,  2 C , a  3, 5
(a  3) 2 (a  5) (a  3) 2 (a  5)
(a  6)(a  5) (a  6)(a  5)
B , a  5,  2 D , a  3,  2
a2 a2
____ 11. Add or subtract. Simplify if possible.
6 1
 2
t  7 t  49

7 6t  41
A C
(t  7)(t  7) (t  7)(t  7)
6t  43 7
B D
(t  7)(t  7) t 2  t  56

4
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

____ 12. Add or subtract. Simplify if possible.

p 2  11p  28 6

p 2  4p  21 p3

p4
A C p  10
p3
p  10 p 2  11p  22
B 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 x 2  7x  21
A C
2x 2  10x  18 (x  1)(x  4)
2x 2  7x  21 2x 2  11x  5
B D
(x  1)(x  4) (x  1)(x  4)
____ 14. Simplify the complex fraction.
4 3

2a 3a
1 1

4a a

4 1 5
A B 2 C D
5 2 4
d3
d 2  d  20
____ 15.
d7
d4
d3 (d  3)(d  7)
A C
(d  7)(d  5) (d  4) 2 (d  5)
(d  3)(d  7) (d  3)(d  5)
B D
(d  4)(d  5) (d  7)(d  5)

5
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

____ 16. Solve the equation. Check the solution.

1 5

x1 x2

1 5 7
A  B 7 C  D 
2 6 6
____ 17. Solve the equation. Check the solution.
a 2 1
 
a 2  36 a  6 a6

A –9 B –6 C –9 and –6 D 6
____ 18. Solve the equation. Check the solution.
6 1
2
  1
x 9 x3

1  73
A 4 B 2 C D 3 or –4
2
____ 19. Solve the equation. Check the solution.
1 5
  5
6y 2y

4 8 8 3
A  B C  D 
15 3 15 20

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
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

21. Simplify
7m2  28n 2
28n 2  7m2
22. Simplify.
x 2  x  xy  y x 2  2xy  y 2

x 2  6x  7 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.

x2  4
f  x 
x2

p(x)
26. Given f(x)  where q(x)  0. How do you determine if the function has a horizontal asymptote? a
q(x)
vertical asymptote? a hole?

27. Simplify.
1 xy  ay  1  2
 

ay  3a  2xy  6x a 2  4x 2  y  3 
 

8
 ID: A

ALGEBRA 2 HONORS: CHAPTER 9 EXAM

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: L2

REF: 9-3 Rational Functions and Their Graphs
OBJ: 9-3.1 Properties of Rational Functions TOP: 9-3 Example 1
KEY: rational function | point of discontinuity
2. ANS: A PTS: 1 DIF: L2
REF: 9-3 Rational Functions and Their Graphs
OBJ: 9-3.1 Properties of Rational Functions TOP: 9-3 Example 2
KEY: asymptote | vertical asympotote | rational function | graphing | hole in the graph of a function
3. ANS: A PTS: 1 DIF: L2
REF: 9-3 Rational Functions and Their Graphs
OBJ: 9-3.1 Properties of Rational Functions TOP: 9-3 Example 3
KEY: asymptote | graphing | rational function | horizontal asymptote
4. ANS: A PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.1 Simplifying Rational Expressions STA: CA A2 7.0
TOP: 9-4 Example 1
KEY: rational expression | simplifying a rational expression | restrictions on a variable
5. ANS: B PTS: 1 DIF: L3 REF: 9-4 Rational Expressions
OBJ: 9-4.1 Simplifying Rational Expressions STA: CA A2 7.0
TOP: 9-4 Example 1
KEY: rational expression | simplifying a rational expression | restrictions on a variable
6. ANS: C PTS: 1 DIF: L2
REF: 9-3 Rational Functions and Their Graphs OBJ: 9-3.2 Graphing Rational Functions
TOP: 9-3 Example 4 KEY: graphing | rational function
7. ANS: A PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.2 Multiplying and Dividing Rational Expressions STA: CA A2 7.0
TOP: 9-4 Example 3
KEY: simplifying a rational expression | restrictions on a variable | multiplying rational expressions
8. ANS: A PTS: 1 DIF: L3
REF: 9-3 Rational Functions and Their Graphs OBJ: 9-3.2 Graphing Rational Functions
TOP: 9-3 Example 4 KEY: graphing | rational function
9. ANS: D PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.2 Multiplying and Dividing Rational Expressions STA: CA A2 7.0
TOP: 9-4 Example 3
KEY: simplifying a rational expression | restrictions on a variable | multiplying rational expressions
10. ANS: D PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.2 Multiplying and Dividing Rational Expressions STA: CA A2 7.0
TOP: 9-4 Example 4 KEY: restrictions on a variable | dividing rational expressions

1
 ID: A

11. ANS: B PTS: 1 DIF: L2

REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.1 Adding and Subtracting Rational Expressions STA: CA A2 7.0
TOP: 9-5 Example 3
KEY: simplifying a rational expression | adding rational expressions
12. ANS: B PTS: 1 DIF: L2
REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.1 Adding and Subtracting Rational Expressions STA: CA A2 7.0
TOP: 9-5 Example 4
KEY: simplifying a rational expression | subtracting rational expressions
13. ANS: B PTS: 1 DIF: L3
REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.1 Adding and Subtracting Rational Expressions STA: CA A2 7.0
TOP: 9-5 Example 3
KEY: simplifying a rational expression | adding rational expressions
14. ANS: A PTS: 1 DIF: L2
REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.2 Simplifying Complex Fractions STA: CA A2 7.0
TOP: 9-5 Example 5
KEY: complex fraction | simplifying a rational expression | simplifying a complex fraction
15. ANS: A PTS: 1 DIF: L2
REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.2 Simplifying Complex Fractions STA: CA A2 7.0
TOP: 9-5 Example 5
KEY: dividing rational expressions | simplifying a complex fraction
16. ANS: D PTS: 1 DIF: L2 REF: 9-6 Solving Rational Equations
OBJ: 9-6.1 Solving Rational Equations STA: CA A2 7.0 TOP: 9-6 Example 1
KEY: rational equation
17. ANS: A PTS: 1 DIF: L2 REF: 9-6 Solving Rational Equations
OBJ: 9-6.1 Solving Rational Equations STA: CA A2 7.0 TOP: 9-6 Example 2
KEY: rational equation | no solutions
18. ANS: A PTS: 1 DIF: L2 REF: 9-6 Solving Rational Equations
OBJ: 9-6.1 Solving Rational Equations STA: CA A2 7.0 TOP: 9-6 Example 2
KEY: rational equation | no solutions
19. ANS: C PTS: 1 DIF: L2 REF: 9-6 Solving Rational Equations
OBJ: 9-6.1 Solving Rational Equations STA: CA A2 7.0 TOP: 9-6 Example 2
KEY: 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