1. Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions
Objectives of this Section
Evaluate Exponential Functions
Graph Exponential Functions
Define the Number e
Solve Exponential Equations

2. An exponential function is a function of the form
where a is a positive real number (a > 0) and a The domain of f is the set of all real numbers.

3. Using a calculator to evaluate an exponential function
Example: Find
On a scientific calculator: 2 yx
1.41
On a graphing calculator: 2 ^
1.41 =

4. The graph of a basic exponential function can be readily obtain using point plotting.
(1, 6) 6x 3x
(1, 3)
(-1, 1/3)
(-1, 1/6)
(0, 1)

5. Summary of the Characteristics of the graph of
Domain: All real numbers
Range: (0, )
No x-intercepts
y-intercept: (0,1)
Horizontal asymptote: y = 0 as x
Increasing function
One-to-one

6. Summary of the Characteristics of the graph of
Domain: All real numbers
Range: (0, )
No x-intercepts
y-intercept: (0,1)
Horizontal asymptote: y = 0 as x
Decreasing function
One-to-one

7. (-1, 6)
(-1, 3)
(0, 1)
(1, 1/3)
(1, 1/6)

8. Graph and determine the domain, range, and horizontal asymptote of f.
(0, 1)
(1, 3)
(0, 1)
(-1, 3)

9. Domain: All real numbers
(-1, 5)
(0, 3)
y = 2
Domain: All real numbers
Range: { y | y >2 } or (2, )
Horizontal Asymptote: y = 2

12. Solve the following equations for x.