Pre-Algebra

12-6 Exponential Functions

Warm UpWrite the rule for each linear function.

1.

2.

f(x) = -5x - 2

f(x) = 2x + 6

Pre-Algebra

12-6 Exponential Functions

Pre-Algebra

12-6 Exponential Functions

Learn to identify and graph exponential functions.

Pre-Algebra

12-6 Exponential Functions

An exponential function has the form f(x) = p ax, where a > 0 and a ≠ 1. If the input values are the set of whole numbers, the output values form a geometric sequence. The y-intercept is f(0) = p. The expression ax is defined for all values of x, so the domain of f(x) = p ax is all real numbers.

Pre-Algebra

12-6 Exponential Functions

Create a table for the exponential function, and use it to graph the function.

A. f(x) = 3 2x

Example A: Graphing an Exponential Function

3 20 = 3 1

3 21 = 3 2

3 22 = 3 4

3 2-2 = 3 14

3 2-1 = 3 12

x y

–2

–1

0

1

2

3 43 2

3

6

12

Pre-Algebra

12-6 Exponential Functions

Example B: Graphing an Exponential Function

Create a table for the exponential function, and use it to graph the function.

B. f(x) = 4 1 2

x

x y

–2

–1

0

1

2

4

2

1

16

8

4 = 4 41 2

–2

4 = 4 21 2

–1

4 = 4 11 2

0

4 = 4 1 2

1 1 2

4 = 4 1 2

2 1 4

Pre-Algebra

12-6 Exponential Functions

Create a table for the exponential function, and use it to graph the function.

C. f(x) = 2x

Example C

20

21

2-2

2-1

x y

–2

–1

0

1

2

1 41 2

1

2

4 22

Pre-Algebra

12-6 Exponential Functions

Create a table for the exponential function, and use it to graph the function.

D. f(x) = 2x+ 1

Example D

20 + 1

21 + 1

2-2 + 1

x y

–2

–1

0

1

2

5 43 2

2

3

5 22 + 1

2-1 + 1

Pre-Algebra

12-6 Exponential Functions

If a > 1, the output f(x) gets larger as the input x gets larger. In this case, f is called an exponential growth function.

Pre-Algebra

12-6 Exponential Functions

Lesson Review: Part 1

1. Create a table for the exponential function

f(x) = , and use it to graph the

function.

3 1 2

x

x y

–2 12

–1 6

0 3

1

2 3 4

3 2