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
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