Ch. 8 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the given expression.
____
____
1.
a.
c.
b.
d.
a.
c.
b.
d.
2.
Simplify the given expression.
____
3.
a.
c.
b.
d.
Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of the
rational function.
____
4.
a.
b.
c.
d.
asymptotes:
asymptotes:
asymptotes:
asymptotes:
; hole:
; hole:
;
, no holes
;
, no holes
Graph the rational function.
____
5. f(x) =
y
a.
–24 –20 –16 –12 –8
____
20
16
16
12
12
8
8
4
4
–4
–4
4
8
12
16
20
24
–24 –20 –16 –12 –8
x
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
–24
–24
20
16
16
12
12
8
8
4
4
4
8
12
16
20
24 x
–24 –20 –16 –12 –8
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
–24
–24
12
16
20
24 x
4
8
12
16
20
24
x
6. Suppose y varies jointly as x and z. Find y when x = 2 and z = 11, if y = 160 when x = 3 and z = 8. Round your
answer to the nearest hundredth, if necessary.
a. 1,173.33
c. 13.33
b. 146.67
d. 174.55
Solve the given equation. Round answers to the nearest hundredth, if necessary.
____
8
24
20
–4
–4
4
y
d.
24
–24 –20 –16 –12 –8
24
20
y
b.
y
c.
24
7.
a. 2.24
b. 0.21
Short Answer
c. 0.24
d. 0.19
8. A raffle prize of
dollars is to be divided among 7x people. Write an expression for the amount of
money that each person will receive.
9. Graph the rational function
Ch. 8 Review
Answer Section
MULTIPLE CHOICE
1. ANS: C
To divide two rational expressions, multiply by the reciprocal of the divisor.
Feedback
A
B
C
D
Did you perform all the mathematical actions?
Did you divide correctly?
Correct!
To simplify the values, divide the denominator by b3, not by b4.
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.2 Simplify rational expressions with division.
STA: {Key}7.0
TOP: Simplify rational expressions with division.
KEY: Rational Expressions | Divide Rational Expressions
MSC: Key
2. ANS: B
Express the question as a division expression, and then multiply by the reciprocal of the divisor.
Feedback
A
B
C
D
The numerator and the denominator are interchanged.
Correct!
Did you eliminate all the common factors?
Did you simplify correctly?
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.3 Simplify complex fractions.
STA: {Key}7.0
TOP: Simplify complex fractions.
KEY: Complex Fractions
MSC: Key
3. ANS: C
Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator
and subtract the numerators.
Feedback
A
B
C
D
Find the common denominator and then subtract the numerators.
Did you simplify properly?
Correct!
Did you find the correct LCD?
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.3 Subtract rational expressions.
STA: {Key}7.0
TOP: Subtract rational expressions.
KEY: Rational Expressions | Subtract Rational Expressions
MSC: Key
4. ANS: D
If the rational expression of a function is written in simplest form and the function is undefined for x = a, then
x = a is a vertical asymptote.
Feedback
A
B
C
D
Did you find the correct asymptotes?
What does point discontinuity mean?
Check the value of the asymptotes.
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 8-3
OBJ: 8-3.1 Determine the limitations of domains and ranges of the graphs of rational functions.
STA: {Key}7.0
TOP: Determine the limitations of domains and ranges of the graphs of rational functions.
KEY: Graph Rational Functions | Vertical Asymptotes | Point Discontinuity
MSC: Key
5. ANS: A
Draw the vertical asymptote, make a table of values, plot the points, and draw the graph.
Feedback
A
B
C
D
PTS:
STA:
MSC:
6. ANS:
Correct!
You have taken the negative value for plotting the graph.
Where is teh vertical asymptote?
Graph the equation, not the inverse of the equation.
1
{Key}7.0
Key
B
DIF: Advanced
REF: Lesson 8-3
TOP: Graph rational functions.
OBJ: 8-3.2 Graph rational functions.
KEY: Graph Rational Functions
Use one set of proportions to find the other set of corresponding values in the equation
.
Feedback
A
B
C
D
Did you substitute the values of all the variables?
Correct!
Have you used all the values of the variables?
Did you use the correct equation for joint variation?
PTS: 1
DIF: Advanced
REF: Lesson 8-4
OBJ: 8-4.2 Recognize and solve joint variation problems.
TOP: Recognize and solve joint variation problems.
KEY: Joint Variation
7. ANS: C
Find the least common denominator and multiply both sides by it.
Feedback
A
B
C
D
Did you substitute the values correctly?
Did you solve the equation correctly?
Correct!
Did you perform the correct arithmetic operation?
PTS: 1
DIF: Advanced
REF: Lesson 8-6
STA: {Key}7.0
TOP: Solve rational equations.
KEY: Rational Equations | Solve Rational Equations
OBJ: 8-6.1 Solve rational equations.
MSC: Key
SHORT ANSWER
8. ANS:
dollars
To find the amount received by each person, divide the amount of raffle prize by the total number of people.
In order to divide the two rational expressions, multiply by the reciprocal of the divisor.
PTS: 1
STA: {Key}7.0
MSC: Key
9. ANS:
DIF: Basic
REF: Lesson 8-2
TOP: Solve multi-step problems.
OBJ: 8-2.4 Solve multi-step problems.
KEY: Multi-step | Problem Solving
f( x)
6
5
4
3
2
1
–6
–5
–4
–3
–2
O
–1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
Draw the vertical asymptotes. Make a table of values and plot the points. Use the points plotted along with the
vertical asymptotes to graph the function.
PTS: 1
STA: {Key}7.0
MSC: Key
DIF: Advanced
REF: Lesson 8-3
TOP: Solve multi-step problems.
OBJ: 8-3.3 Solve multi-step problems.
KEY: Multi-step | Problem Solving