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Graphs of Exponential Functions

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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  1. Graphs of Exponential Functions Lesson 3.3

  2. 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

  3. How Does a*bt Work? • Conclusion • All the graphs cross the y-axis at A • The graph is steeper for some x

  4. 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

  5. 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

  6. 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

  7. How Does a*btWork? • Results when 0 < b < 1 • Graph is up to the left, down to the right

  8. Horizontal Asymptotes • When b > 1, f(x) 0 as x  -∞ • When 0 < b < 1, f(x) 0 as x +∞

  9. 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 ???

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

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