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CHAPTER 3
Exponential and Logarithmic Functions
Section 3.1
Exponential Functions and Their Graphs
■ You should know that a function of the form y a x , where a > 0, a 1, is called an exponential function
with base a.
■ You should be able to graph exponential functions.
■ You should be familiar with the number e and the natural exponential function fx e x .
■ You should know formulas for compound interest.
(a) For n compoundings per year:
A P 1 r n nt .
(b) For continuous compoundings: A Pe rt .
Vocabulary Check
1. algebraic 2. transcendental 3. natural exponential, natural
4. A P 1 5. A Pe
n r nt
rt
1. 3.4 6.8 4112.033 2. 1.2 13 1.063
3. 5 0.006
4. 8.6 32 8.6 32 9220.217
6.
5.
gx 5 x
fx 3 2 x
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x 2 1 0 1 2
x 2 1 0 1 2
y
1 1
1 5 25
y
4 2
1
25
Asymptote: y 0
Intercept: 0, 1
Increasing
4
3
2
1
–2 –1 1 2
y
5
x
9
Asymptote: y 0
Intercept: 0, 1
Increasing
−5 −4 −3 −2 −1
9
8
7
6
5
4
3
2
y
3
1
2
3
4
5
3
2
x
9
4
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