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 Set the window at -5<x<5 -10<y<10 Set the window at -5<x<5 -10<y<10

How Does a*b t Work? Conclusion  All the graphs cross the y-axis at A  The graph is steeper for some x

How Does a*b t Work? Now let’s try to see what happens when we change the value for b Specify the following in the Y= screen 2*1.1 x 2*1.5 x 2*2.0 x 2*2.5 x 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*b t 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*b t Work? Consider 0 < b < 1 Graph the following: 2*0.75 x 2*0.5 x 2*0.25 x 2*0.1 x Set the window at -5<x<5 -10<y<10 Set the window at -5<x<5 -10<y<10

How Does a*b t 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