7.3 Notes – Use Functions Involving e. A number that occurs frequently in nature is one that results when n gets infinitely large in the expression. As.

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Presentation transcript:

7.3 Notes – Use Functions Involving e

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 ≈ 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.

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

Simplify the expression. 3. ===

Simplify the expression. 4. = 2 e2e2 =

Simplify the expression. 5. =

Simplify the expression. 6. =

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

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

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

Graph the function. Identify the equation of the asymptote, domain, and range. xy Asymptote: _______________ Domain: __________________ Range: ___________________ y = 0

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

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

Graph the function. Identify the equation of the asymptote, domain, and range. xy Asymptote: _______________ Domain: __________________ Range: ___________________ y = 0

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

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