Exponential and Logarithmic Functions: Comparing Logarithmic and Exponential Functions

Warm-Up Icon Section Warm-Up

As we begin to work with logarithmic and exponential functions, let’s begin with a warm-up.
Analyze the following function, f(x) = 5x.
1. In your notes find the y-values for the function by using the following table:


x

y

-2

 

-1

 

 0

 

 1

 

 2

 

 3

 

 4

 

Solution:
For each, substitute the x value in f(x) = 5x.  You may use a calculator to help you find the answer.
Example:  f(-2) = 5-2 = 0.04


x

y

-2

0.04

-1

0.2

0

1

1

5

2

25

3

125

4

625

2. Graph this function using the points in the table.
Solution:

3. Next, graph the inverse function by interchanging the x- and y-values.

Solution:
Inverse function


x

y

0.04

-2

0.2

-1

1

0

5

1

25

2

125

3

625

4

4. Take notes about how these two functions look, their properties, and domain and range.