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 * 1.1X

2 * 1.1X 0.5 * 1.1X

1.5 * 1.1X

Set the window at

-5<x<5-10<y<10

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*bt Work?

• 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

Set the window at

-5<x<5-10<y<10

Set the window at

-5<x<5-10<y<10

Verify conclusions with spreadsheet from previous

lesson.

Verify conclusions with spreadsheet from previous

lesson.

How Does a*bt Work?

• 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*0.75x 2*0.5x

2*0.25x 2*0.1x

Set the window at

-5<x<5-10<y<10

Set the window at

-5<x<5-10<y<10

How Does a*bt Work?

• 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