coordinated algebra unit 3 part b. what is an exponential function?

Coordinated AlgebraUnit 3 Part B

What is an Exponential Function?

Examples…

Applications…

Population Growth

Science (Bacterial Growth, Radiation, Half-Life,

etc.)

Investments/Finance

Appreciation and Depreciation

Let’s examine exponential functions. They are different than any of the other types of functions we’ve studied because the independent variable is in the exponent.

xxf 2

Let’s look at the graph of this function by plotting some points. x 2x

3 8 2 4 1 2 0 1

-1 1/2 -2 1/4 -3 1/8

2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8

7

123456

8

-2-3-4-5-6-7

2

121 1 f

Recall what a negative exponent means:

BASE

xxf 2

xxf 3

Compare the graphs 2x, 3x , and 4x

Characteristics about the Graph of an Exponential Function where a > 1 xaxf

What is the domain of an exponential function?

1. Domain is all real numbers

xxf 4

What is the range of an exponential function?

2. Range is positive real numbers

What is the x intercept of these exponential functions?

3. There are no x intercepts because there is no x value that you can put in the function to make it = 0

What is the y intercept of these exponential functions?

4. The y intercept is always (0,1) because a 0 = 1

5. The graph is always increasing

Are these exponential functions increasing or decreasing?

6. The x-axis (where y = 0) is a horizontal asymptote for x -

Can you see the horizontal asymptote for these functions?

xxf 2

xxf 3

xexf