1. 6.2 Exponential Functions

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

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

4. a >1 Summary of the characteristics of the graph of
The domain is all real numbers. Range is set of positive numbers.
No x-intercepts; y-intercept is 1.
The x-axis (y=0) is a horizontal asymptote as
a>1, is an increasing function and is one-to-one.
The graph contains the points (0,1); (1,a), and (-1, 1/a).
The graph is smooth continuous with no corners or gaps.

5. (-1, 6)
(-1, 3)
(0, 1)
(1, 1/3)
(1, 1/6)

6. 0 <a <1 Summary of the characteristics of the graph of
The domain is all real numbers. Range is set of positive numbers.
No x-intercepts; y-intercept is 1.
The x-axis (y=0) is a horizontal asymptote as
0<a<1, is a decreasing function and is one-to-one.
The graph contains the points (0,1); (1,a), and (-1, 1/a).
The graph is smooth continuous with no corners or gaps.

8. (1, 3)
(0, 1)

9. (-1, 3)
(0, 1)

10. (-1, 5)
(0, 3)
y = 2

11. Domain: All real numbers
Range: { y | y >2 } or
Horizontal Asymptote: y = 2

12. The number e is defined as the number that the expression
In calculus this expression is expressed using limit notation as

15. Exponential Equations

16. Solve: