1. Exponential Functions
Section
12.3
Exponential Functions

2. Exponential Function
A function of the form
f(x) = bx
is called an exponential function if b > 0, b is not 1, and x is a real number.

3. Exponential Functions
We can graph exponential functions of the form f(x) = 3x, g(x) = 5x or h(x) = (½)x by substituting in values for x, and finding the corresponding function values to get ordered pairs.
We would find all graphs satisfy the following properties:
one-to-one function
y-intercept (0, 1)
no x-intercept
domain is (−, )
range is (0, )

4. Example
Graph the exponential functions f(x) = 2x and g(x) = 4x on the same set of axes.
Continued

5. Example Graph the exponential functions and on the same set of axes.
Continued

6. Graphs of Exponential Functionsy
We would find a pattern in the graphs of all the exponential functions of the type bx, where b > 1.

7. Graphs of Exponential Functionsy
We would find a pattern in the graphs of all the exponential functions of the type bx, where 0 < b < 1.

8. Example
Graph the exponential function

9. Uniqueness of bx
Let b > 0 and b  1. Then bx = by is equivalent to x = y.

10. Example
Solve each equation for x.
a. 6x = b. 92x+1 = 81 c.

11. Example
Solve 43x-6 = 322x