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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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Presentation Transcript
how does a b t work
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
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 b t work4
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 b t work5
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 b t work6
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 b t work7
How Does a*btWork?
  • Results when 0 < b < 1
    • Graph is up to the left, down to the right
horizontal asymptotes
Horizontal Asymptotes
  • When b > 1, f(x) 0 as x  -∞
  • When 0 < b < 1, f(x) 0 as x +∞
restrictions on b
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
Assignment
  • Lesson 3.3A
  • Page 127
  • Exercises 1 – 25 odd
  • Lesson 3.3B
  • Page 128
  • Exercises 27 – 41 odd
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