1. 7.3 Notes – Use Functions Involving e

2. A number that occurs frequently in nature is one that results when n gets infinitely large in the expression. As n gets larger and larger, it becomes ≈ 2.71828. Since this expression occurs so often, the limit, or the number it approaches as n approaches infinity, is given the special symbol e, after its discoverer, Leonard Euler. We can use like any other number to multiply, divide, use as a base, or as an exponent.

3. Simplify the expression. 1. == 2. 4 e = 4e4e

4. Simplify the expression. 3. ===

5. Simplify the expression. 4. = 2 e2e2 =

6. Simplify the expression. 5. =

7. Simplify the expression. 6. =

8. Use a calculator to evaluate the expression to 3 decimals. 7.  54.598

9. Use a calculator to evaluate the expression to 3 decimals. 8.  1.828

10. Use a calculator to evaluate the expression to 3 decimals. 9.  2.834

11. Graph the function. Identify the equation of the asymptote, domain, and range. xy Asymptote: _______________ Domain: __________________ Range: ___________________ -2 0 1 2 0.135 0.368 1 2.718 7.389 y = 0

12. Identify the parent graph, describe the transformations, and then graph the function. Identify the equation of the asymptote, domain, and range. 10. Parent graph: Transformations: Eq. of asymptote: Domain: Range: Right 3, up 1 y = 1

13. Identify the parent graph, describe the transformations, and then graph the function. Identify the equation of the asymptote, domain, and range. 11. Parent graph: Transformations: Eq. of asymptote: Domain: Range: Reflect x-axis, up 2 y = 2

14. Graph the function. Identify the equation of the asymptote, domain, and range. xy Asymptote: _______________ Domain: __________________ Range: ___________________ -2 0 1 2 0.271 0.736 2 5.437 14.778 y = 0

15. Identify the parent graph, describe the transformations, and then graph the function. Identify the equation of the asymptote, domain, and range. 12. Parent graph: Transformations: Eq. of asymptote: Domain: Range: Left 2, down 1 y = -1

16. Identify the parent graph, describe the transformations, and then graph the function. Identify the equation of the asymptote, domain, and range. 12. Parent graph: Transformations: Eq. of asymptote: Domain: Range: Reflect x-axis y = 0