MATH 14 – PLANE TRIGONOMETRY

EXPONENTIAL FUNCTIONS

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Exponential Function

An example of transcendental function

Exponential functions are used to model a variety of real world phenomena

Growth of populations

Radioactive decay

Epidemics

Absorption of light as it passes through a medium

Magnitudes of sound and earthquakes

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Exponential Functions

If b > 0 and b ≠ 1, then the exponential function with

base b is the function f defined by

base

exponent

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Properties of

The x-axis is the horizontal asymptote of the graph.

The y-intercept of the graph is 1.

The graph is increasing when b > 1, while the graph is decreasing if 0 < b < 1.

The function is one-to-one.

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1,0 b,1

5

1,0 2,1

6

1,0

2

1,1

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General Form

The horizontal asymptote of the graph is y = k.

The graph is above the asymptote if a > 0 while the

graph is below the asymptote if a < 0.

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How to sketch the graph?

1. Find the horizontal asymptote. How?

2. Determine two arbitrary points. What points?

3. Locate the points.

4. Use the asymptote-two-point technique!

. | 0a x x h . | 1b x x h

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Illustrations 10

2,2 4,3

1y

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Illustrations 12

3,1 2,04y

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Illustrations 14

5,5

7,4

4y

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Illustrations 16

3,5

1,4

4y

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TRY THESE! Find the domain, range, horizontal asymptote and

sketch the graph of the following:

1.

2.

3.

4.

2( ) 3 1xy f x

53

( ) 24

x

y h x

2 1( ) 5 2xy g x

2( ) 3 1xy f x

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