1. Exponential Functions
Pre-Algebra
12-6
Exponential Functions
Warm Up
Write the rule for each linear function. 1. 2.
f(x) = -5x - 2
f(x) = 2x + 6

2. Learn to identify and graph exponential functions.

3. 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.

4. Example A: Graphing an Exponential Function
Create a table for the exponential function, and use it to graph the function.
A. f(x) = 3  2x x y –2 –1 1 2
3 4
3  2-2 = 3  1 4
3  2-1 = 3  1 2
3 2 3
3  20 = 3  1 6
3  21 = 3  2 12
3  22 = 3  4

5. 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 1 2
4  = 4  4
1 2 –2 16
4  = 4  2
1 2 –1 8
4  = 4  1
1 2 4
4  = 4 
1 2 1 2
4  = 4 
1 2 2
1 4 1

6. Example C
Create a table for the exponential function, and use it to graph the function.
C. f(x) = 2x x y –2 –1 1 2
1 4
2-2
1 2
2-1 1 20 2 21 4 22

7. Example D
Create a table for the exponential function, and use it to graph the function.
D. f(x) = 2x+ 1 x y –2 –1 1 2
5 4
3 2 2
20 + 1 3
21 + 1 5
22 + 1

8. If a > 1, the output f(x) gets larger as the input x gets larger
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.

9. 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 3 1 2
3 4
3 2