Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions

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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

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An exponential function is a function of the form
where a is a positive real number (a gt 0) and a
1. The domain of f is the set of all real
numbers.
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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...
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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)
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Domain All real numbers Range (0, ) No
x-intercepts y-intercept (0,1) Horizontal
asymptote y 0 as x Increasing
function One-to-one
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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
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(-1, 6)
(-1, 3)
(0, 1)
(1, 1/3)
(1, 1/6)
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Graph and determine the
domain, range, and horizontal asymptote of f.
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(-1, 5)
(0, 3)
y 2
Domain All real numbers
Range y y gt2 or (2, )
Horizontal Asymptote y 2
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Solve the following equations for x.