Graph Exponential Growth Functions

4.4 (M2)

4.4-4.5 Quiz: FridayComputer Lab (C28): Monday

**You need

graph paper**

Vocabulary

• An exponential function has the form y = abx, where a ≠ 0 and the base b is a positive number other than 1.

• If a > 0 and b > 1, the function y = abx is an exponential growth function– and b is called the growth factor.

Vocabulary

• An asymptote is a line that a graph approaches more and more closely (but will never actually touch!)

• The end behavior of a function’s graph is the behavior of the graph as x approaches positive or negative infinity.

Make a table of values.STEP 1

STEP 2 Plot the points from the table.

Graph y = 2x.

Example 1:

EXAMPLE 2

Graph the function.

SOLUTION

Plot and (1, 2) .Then,

from left to right, draw a curve that begins just above the x-axis, passes through the two points, and moves up to the right.

0, 12

a.

1a. 4

2xy

EXAMPLE 2 Cont’d

Graph the function.

b. y = – 52

x

Plot (0, –1) and .

Then,from left to right, draw a curve that begins just below the x-axis, passes through the two points,and moves down to the right.

b. 1, – 52

SOLUTION

Graph State the domain and range.

SOLUTION

Example 314 2 3.xy

• Begin by sketching the graph y = 4 ● 2x

• Then translate the graph: y = 4 ● 2x – 1 – 3

y = 4 2x

Example 3 Cont’d

•Domain?

•Range?

•Asymptote?

Your Turn

Graph each function below. State the

Domain, range, and asymptote.

• y = 5x

• f(x) = 1/3 ● 4x

• y = 2x + 1 – 1

Your Turn: Answers

Domain: all real #sRange: y > 0Asym.: y = 0

Domain: all real #sRange: y > 0Asym.: y = 0

Domain: all real #sRange: y > -1Asym.: y = -1

Practice Problems

• Out of your purple (M2) book

Pg. 122 #1-17