Post on 04-Jan-2016
Chapter 3Exponential and
Logarithmic Functions
Chapter 3.1Exponential Functions
Exponential Functions
exponentialfunction with basIf 0 and 1, then the
is defined b ye
x
b
f x
b
b
b
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
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
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
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
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.
Exponential Functions
Form:
H.A.: is one-to-one.
P xy f x ab k
y kf
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
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
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
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
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
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
End of Chapter 3.1