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7.3 Notes – Use Functions Involving e

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 ≈ 2.71828 . Since this expression occurs so often, the limit, or the number it

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7.3 Notes – Use Functions Involving e

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  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. 4 4 e 2. = e

  4. Simplify the expression. 3. = = =

  5. Simplify the expression. 4. e2 = = 2

  6. Simplify the expression. 5. =

  7. Simplify the expression. 6. =

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

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

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

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

  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. -2 0.271 -1 0.736 0 2 1 5.437 2 14.778 y = 0 Asymptote: _______________ Domain: __________________ Range: ___________________

  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

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