Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.
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Transcript of Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.
![Page 1: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/1.jpg)
Chapter 3Exponential and
Logarithmic Functions
![Page 2: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/2.jpg)
Chapter 3.1Exponential Functions
![Page 3: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/3.jpg)
Exponential Functions
exponentialfunction with basIf 0 and 1, then the
is defined b ye
x
b
f x
b
b
b
![Page 4: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/4.jpg)
Example 3.1.1
If 2 , complete the given table.xf x
x f (x)0 11 22 43 84 16
x f (x)-1 1/2-2 1/4-3 1/8-4 1/16
![Page 5: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/5.jpg)
x -4 -3 -2 -1 0 1 2 3 4
f (x) 1/16 1/8 1/4 1/2 1 2 4 8 16
0,
H.A.: 0 is increasing.
Dom f R
Rng f
yf
is one-to-one.f
![Page 6: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/6.jpg)
Example 3.1.2
1If , complete the given table.
2
x
f x
x f (x)0 11 1/22 1/43 1/84 1/16
x f (x)-1 2-2 4-3 8-4 16
![Page 7: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/7.jpg)
x -4 -3 -2 -1 0 1 2 3 4
f (x) 16 8 4 2 1 1/2 1/4 1/8 1/16
0,
H.A.: 0 is decreasing.
Dom f R
Rng f
yf
is one-to-one.f
![Page 8: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/8.jpg)
Exponential Functions
Form:
where and are constantsalso, 0 and 1.
, if 0
, if 0
P xy f x ab k
a kb b
Dom f R
Rng fk a
k a
Math 17: assume P is linear polynomial.
![Page 9: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/9.jpg)
Exponential Functions
Form:
H.A.: is one-to-one.
P xy f x ab k
y kf
![Page 10: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/10.jpg)
Example 3.1.3
11Given 1
2a. Find the domain and range of .
1,
b. Find the horizontal asymptote.1
x
f x
f
Dom f R Rng f
y
![Page 11: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/11.jpg)
1
c. Sketch the graph of .
11
2H.A.: 1
1,
x
f
f x
y
Dom f R
Rng f
x 1 2y 2 3/2
1y
![Page 12: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/12.jpg)
Example 3.1.4
1Given 2 3 1
a. Find the domain and range.
,1
b. Find the horizontal asymptote.1
xg x
Dom g R Rng g
y
![Page 13: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/13.jpg)
1
c. Sketch the graph of .
2 3 1
H.A.: 1
,1
x
g
g x
y
Dom g R
Rng g
x 1 0y -1 -5
1y
![Page 14: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/14.jpg)
Example 3.1.5
11
1
2Given 2 2 5 2
52 5 2
a. Find the domain and range.
2,
b. Find the horizontal asymptote.2
xx
x
h x
h x
Dom h R Rng h
y
![Page 15: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/15.jpg)
1
c. Sketch the graph of .
2 5 2
H.A.: 2
2,
x
h
h x
y
Dom f R
Rng f
x 1 0y 0 8
2y
![Page 16: Chapter 3 Exponential and Logarithmic Functions. Chapter 3.1 Exponential Functions.](https://reader038.fdocuments.in/reader038/viewer/2022102809/56649f135503460f94c27361/html5/thumbnails/16.jpg)
End of Chapter 3.1