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