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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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Graphs of Exponential Functions

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Graphs of exponential functions l.jpg

Graphs of Exponential Functions

Lesson 3.3


How does a b t work l.jpg

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 b t work3 l.jpg

How Does a*bt Work?

  • Conclusion

    • All the graphs cross the y-axis at A

    • The graph is steeper for some x


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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


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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


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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


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How Does a*btWork?

  • Results when 0 < b < 1

    • Graph is up to the left, down to the right


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Horizontal Asymptotes

  • When b > 1, f(x) 0 as x  -∞

  • When 0 < b < 1, f(x) 0 as x +∞


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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

???


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Assignment

  • Lesson 3.3A

  • Page 127

  • Exercises 1 – 25 odd

  • Lesson 3.3B

  • Page 128

  • Exercises 27 – 41 odd


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