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Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions

Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions. Objectives of this Section Evaluate Exponential Functions Graph Exponential Functions Define the Number e Solve Exponential Equations. An exponential function is a function of the form.

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Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions

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  1. Sullivan Algebra and Trigonometry: Section 5.3Exponential Functions • Objectives of this Section • Evaluate Exponential Functions • Graph Exponential Functions • Define the Number e • Solve Exponential Equations

  2. An exponential function is a function of the form where a is a positive real number (a > 0) and a 1. The domain of f is the set of all real numbers.

  3. Using a calculator to evaluate an exponential function Example: Find 2 1.41 2 yx 1.41 On a scientific calculator: 2 ^ 1.41 On a graphing calculator: 2 1.41 = 2.657371628...

  4. The graph of a basic exponential function can be readily obtain using point plotting. (1, 6) 6x 3x (1, 3) (-1, 1/3) (-1, 1/6) (0, 1)

  5. Summary of the Characteristics of the graph of Domain: All real numbers Range: (0, ) No x-intercepts y-intercept: (0,1) Horizontal asymptote: y = 0 as x Increasing function One-to-one

  6. Summary of the Characteristics of the graph of Domain: All real numbers Range: (0, ) No x-intercepts y-intercept: (0,1) Horizontal asymptote: y = 0 as x Decreasing function One-to-one

  7. (-1, 6) (-1, 3) (0, 1) (1, 1/3) (1, 1/6)

  8. (1, 3) (-1, 3) (0, 1) (0, 1) Graph and determine the domain, range, and horizontal asymptote of f.

  9. (-1, 5) (0, 3) y = 2 Domain: All real numbers Range: { y | y >2 } or (2, ) Horizontal Asymptote: y = 2

  10. Solve the following equations for x.

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