Graphs of Exponential Functions

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# Graphs of Exponential Functions - PowerPoint PPT Presentation

Graphs of Exponential Functions. Lesson 3.3. How Does a*b t Work?. Given f(t) = a * b t What effect does the a have? What effect does the b have? Try graphing the following on the same axes 3 * 1.1 X 0.75 * 1.1 X 2 * 1.1 X 0.5 * 1.1 X 1.5 * 1.1 X.

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## PowerPoint Slideshow about 'Graphs of Exponential Functions' - jera

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### Graphs of Exponential Functions

Lesson 3.3

How Does a*bt Work?
• Given f(t) = a * bt
• What effect does the a have?
• What effect does the b have?
• Try graphing the following on the same axes3 * 1.1X 0.75 * 1.1X2 * 1.1X 0.5 * 1.1X1.5 * 1.1X

Set the window at

-5<x<5-10<y<10

How Does a*bt Work?
• Conclusion
• All the graphs cross the y-axis at A
• The graph is steeper for some x
How Does a*btWork?
• Now let’s try to see what happens when we change the value for b
• Specify the following in the Y= screen2*1.1x 2*1.5x 2*2.0x 2*2.5x

Verify conclusions with spreadsheet from previous lesson.

Set the window at

-5<x<5-10<y<10

How Does a*btWork?
• Results:
• All graphs cross the y-axis at y=2
• If b is low: high to left, shallow up to right
• If b is large: low to the left, steeper sooner on the right
How Does a*bt Work?
• Consider 0 < b < 1
• Graph the following:2*0.75x 2*0.5x 2*0.25x 2*0.1x

Set the window at

-5<x<5-10<y<10

How Does a*btWork?
• Results when 0 < b < 1
• Graph is up to the left, down to the right
Horizontal Asymptotes
• When b > 1, f(x) 0 as x  -∞
• When 0 < b < 1, f(x) 0 as x +∞
Restrictions on b
• Note always b > 0 … cannot have
• Fractional power of b when b < 0
• It is not a continuous function
• Also note that calculator will do some funny things with y = (-2)^x

???

Assignment
• Lesson 3.3A
• Page 127
• Exercises 1 – 25 odd
• Lesson 3.3B
• Page 128
• Exercises 27 – 41 odd