graph exponential growth functions

Graph Exponential Growth Functions

4.4

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.

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.

Example 314 2 3.xy

SOLUTION• 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

4.5 Graph Exponential

Decay Functions

Vocabulary

• An exponential decay function has the form y = abx, where a > 0 and 0 < b < 1.

• The base b of an exponential decay function is called the decay factor.

Example 11

3

x

y

Example 2• Graph y = -3(1/4)x. State the domain and range. Give

the equation for the asymptote.

Example 3• Graph y = 2(2/3)x – 1 + 1. State the domain and

range. Give the equation for the asymptote.

Homework

Worksheet!!!