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Graphs of Exponential Functions

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Graphs of Exponential Functions

Lesson 3.3

- 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

- Conclusion
- All the graphs cross the y-axis at A
- The graph is steeper for some x

- 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

- 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

- 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

- Results when 0 < b < 1
- Graph is up to the left, down to the right

- When b > 1, f(x) 0 as x -∞
- When 0 < b < 1, f(x) 0 as x +∞

- 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

???

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