3.3 Graphs of Exponential Functions

Exponential Growth Graphs•When b > 1 ▫ graph moves away from x-axis quickly from left to right.

•y-intercept is at point (0, a).

Exponential Decay Graphs•When 0< b < 1 ▫ graph moves towards x-axis quickly from left to right.

•y-intercept is at point (0, a).

Asymptotes•An asymptote is a line that a graph approaches (but does not touch) as it moves away from the origin.

•Functions of the formy = a(b)x have horizontal asymptotes at y = 0.

Domain & Range•Domain & Range describe which input/output values will work for a given function.•Domain – set of all input values (x’s)▫Look left and right•Range – set of all output values (y’s)▫Look up and down•Can be written using inequalities.

Example 1:•Identify the following -

•Growth or Decay?

•Domain:

•Range:

•Asymptote:

•y-int:

Example 2:•Identify the following -

•Growth or Decay?

•Domain:

•Range:

•Asymptote:

•y-int:

You Try!•Identify the following -

•Growth or Decay?

•Domain:

•Range:

•Asymptote:

•y-int:

Graphing Exponential Functions•To graph y = a(b)x 1. Make a table2. Plot the points3. Connect with a smooth curve

Be Careful:• Don’t cross the asymptote (y = 0)!!• Check that y-int is (0, a)!!

Example 1:•Graph •State the domain and range.

Example 2:•Graph •State the domain and range.

You Try!

•Graph •State the domain and range.

Example 3:•Graph •State the domain and range.

Example 4:•Graph •State the domain and range.

You Try!•Graph •State the domain and range.

Transformations •Remember: •+ and – mean shift•Changing the input shifts left/right▫Do the opposite!!•Changing the output shifts up/down

•We will call the original function y = a(b)x the “parent function”•Its graph is the “parent graph”

Example 1:•Identify the parent function and describe the transformation on it.

1.

2.

3.

You Try!•Identify the parent function and describe the transformation on it.

1.

2.

3.

To Graph:•Sketch the parent graph with a dashed line.•Shift points and draw final graph. •Example:•Graph •Domain:•Range:

Example 2:

•Graph

•Domain:•Range:

You Try!

•Graph

•Domain: •Range: