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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.

Graphs of Exponential Functions

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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*1.1x2*1.5x2*2.0x2*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*0.75x2*0.5x2*0.25x2*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