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Section 3.1 Exponential Functions and Their Graphs 195
15. fx 2 x 4 rises to the right.
Asymptote: y 4
Intercept: 0, 3
Matches graph (c).
16. fx 2 x 1 is increasing and has 0, 2 intercept.
Matches graph (b).
17.
f x 3 x
18.
f x 2 x
gx 3 x5 f x 5
gx 5 2 x 5 f x
Horizontal shift five units to the right
Vertical shift five units upward
y
y
−3 −2 −1
7
6
5
4
3
2
1
−2
−3
1 2 3 4 5
6 7
x
−5 −4 −3 −2
6
5
3
2
1
−2
−3
−4
1 2 3 4 5
x
19.
f x 3 5 x
gx 3 5 x4 f x 4
Horizontal shift four units to the left, followed by
reflection in x-axis
5
4
3
2
y
20.
f x 0.3 x
gx 0.3 x 5 f x 5
Reflection in x-axis followed by vertical shift
five units upward
7
6
5
y
−6 −5
−2 −1
−2
−3
−4
−5
1 2 3 4
x
1
−4 −3 −2 −1
−2
−3
1
2 3 4 5 6
x
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21.
fx 4 x 22.
gx 4 x2 3 f x 2 3
Horizontal shift two units to the right followed by
vertical shift three units downward
6
5
4
3
2
1
−5 −4 −3 −2 −1 1 2 3 4 5
−2
−4
y
x
fx 1 2 x
gx 1 2 x4
Reflection in the y-axis followed by left shift of
four units
8
7
6
5
4
3
−7 −6 −5 −4 −3 −2 −1 1 2 3
1
y
x
23. e 9.2 9897.129 24. e 34 e 34
25. 50e 40.02 54.164
2.117