LESSON
5.2
Answers for the lesson “Graph Simple
Rational Functions”
Skill Practice
5.
y
1. range; domain
1
21
2. No; the denominator is an
x
exponential expression, not a
polynomial.
The graph lies farther from the
y
3.
1
axes than the graph of y 5 }x and
1
21
is located in quadrants 2 and 4.
Both graphs have the same
asymptotes, domain, and range.
x
The graph lies farther from the
y
6.
1
axes than the graph of y 5 }x .
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Both graphs lie in the 1st and
3rd quadrants and have the same
asymptotes, domain, and range.
1
x
21
y
4.
The graph lies closer to the
2
22
1
axes than the graph of y 5 }x
x
and is located in quadrants 2 and
4. Both graphs have the same
asymptotes, domain, and range.
The graph lies farther from the
1
axes than the graph of y 5 }x .
Both graphs lie in the 1st and
3rd quadrants and have the same
asymptotes, domain, and range.
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153
y
7.
g(x)
9.
0.2
20.2
2
21
x
The graph lies farther from the
The graph lies closer to the
1
1
axes than the graph of y 5 }x and
axes than the graph of y 5 }x .
is located in quadrants 2 and 4.
Both have the same asymptotes,
domain, and range.
Both graphs lie in the 1st and
3rd quadrants and have the same
asymptotes, domain, and range.
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8.
h(x)
10.
f(x)
1
4
21
x
x
The graph lies farther from the
1
axes than the graph of y 5 }x .
Both graphs lie in the first and
third quadrants and have the same
asymptotes, domain, and range.
x
21
The graph lies farther from the
1
axes than the graph of y 5 }x and
is located in quadrants 2 and 4.
Both have the same asymptotes,
domain, and range.
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154
11.
domain: all real numbers
except 1, range: all real numbers
except 0
y
f(x)
14.
1
1
x
2
21
domain: all real numbers
except 0, range: all real numbers
except 3
y
12.
domain: all real numbers
except 22, range: all real numbers except 0
1
21
x
y
15.
22
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x
x
24
domain: all real numbers
except 0, range: all real numbers
except 22
13.
domain: all real numbers
except 0, range: all real numbers
except 27
y
2
21
x
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155
domain: all real numbers
except 7, range: all real numbers
except 0
y
16.
y
19.
1
21
x
1
domain: all real numbers
except 0, range: all real numbers
except 4
21
domain: all real numbers
except 24, range: all real
numbers except 3
y
17.
1
x
y
20.
x
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21
3
x
29
domain: all real numbers
except 22, range: all real
numbers except 0
18.
domain: all real numbers
except 27, range: all real
numbers except 25
g(x)
1
x
1
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156
21.
28
25. The graph should be y 5 },
x
8
not y 5 }x .
y
y
1
1
x
2
x
22
domain: all real numbers
except 4, range: all real numbers
except 21
26. The vertical asymptote should be
x 5 1, not x 5 21.
h(x)
22.
y
1
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21
x
2
2
x
domain: all real numbers
except 9, range: all real numbers
except 9
y
27.
2
2
23. D
x
24. a. The graph will lie farther from
the asymptotes and will be a
reflection in either asymptote.
b. The vertical asymptote is
shifted left 4 units.
domain: all real numbers
except 3, range: all real numbers
except 1
c. The horizontal asymptote is
shifted up 4 units.
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157
domain: all real numbers
except 3, range: all real numbers
except 4
y
28.
2
26
31.
y
x
3
x
22
domain: all real numbers
except 25, range: all real
numbers except 1
y
29.
domain: all real numbers
5
except 2}4, range: all real
1
5
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1
numbers except 2}4
x
f(x)
32.
domain: all real numbers
except 2, range: all real numbers
1
1
4
except }
30.
21
x
y
domain: all real numbers
1
except }3, range: all real numbers
2
22
x
except 2
Algebra 2
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158
Problem Solving
g(x)
33.
43m 1 50
37. c 5 }
m
c
90
22
Average monthly cost
2
x
domain: all real numbers
3
except 2}2 , range: all real
5
numbers except }2
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8 9 m
Months of service
5 months
h(x)
59m 1 100
38. c 5 }
m
10
x
22
domain: all real numbers
except 10, range: all real numbers
except 25
3x 1 1
35. Sample answer: y 5 }
x18
Average monthly cost
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34.
80
c
160
140
120
100
80
60
40
20
0
0 1 2 3 4 5 6 7 8 m
Months of membership
10 months
k(x 2 h)
a
36. f(x) 5 } 1 }
x2h
(x 2 h)
a 1 kx 2 kh
x2h
5 }
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159
39. a. About 14.5 sec. Sample
b. $3333.33; $8571.43; $40,000;
answer: Substitute 25 for T to
find t ø 2.89. Since you are
5 kilometers away, multiply
t by 5 to get 5(2.89) ø 14.5
seconds.
b.
1,480,000
moving away: f* 5 }
740 1 r
b.
2.9
Frequency (Hz)
Time (sec)
f
2200
2150
2.8
2.7
0
0
10
20
30
40
T
about 3.98C
f1
2100
2050
2000
1950
1900
1850
1800
0
Air temperature (8C)
f2
0
12
24
36
48
r
Speed (mi/h)
40. a.
c. The frequency of a sound
y
Cost (thousands of dollars)
1,480,000
41. a. approaching: f* 5 },
740 2 r
t
3.0
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no. Sample answer: The values
are not increasing at a
constant rate.
that is approaching is greater
than that of a sound that is
moving away.
120
90
60
30
0
0
0.2
0.4
0.6
0.8
x
Percent (as a decimal)
domain: 0axa1,
range: 0aya150
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Average speed (knots)
30 1 15t
42. s 5 }
t13
s
16
12
8
4
0
0
4
8
12
16
t
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Time using motor (hr)
Algebra 2
Answer Transparencies for Checking Homework
161