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Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions

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Presentation on theme: "Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions"— Presentation transcript:

1 Sullivan Algebra and Trigonometry: Section 6.3 Exponential 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 The domain of f is the set of all real numbers.

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

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

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

10

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12 Solve the following equations for x.


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