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

4. Summary of the characteristics of the graph of a >1 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, 3) (-1, 6) (0, 1)(1, 1/3)(1, 1/6)

6. Summary of the characteristics of the graph of 0 <a <1 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. (0, 1) (1, 3)

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

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

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

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: