Exponential Growth Exponential Growth and and

Decay Decay FunctionsFunctions

What is an exponential function?What is an exponential function?

An exponential function has the form:

y = abx

Where a is NOT equal to 0 and

The base b is a positive number other than 1

Exponential Growth

a > 0

And

b > 1

b is called the growth factor

Exponential Decay

a > 0

And

0< b < 1

b is called the decay factor

y = abx

Graphing Exponential FunctionsGraphing Exponential FunctionsExample

Is this a growth or decay function???

Graphing Exponential FunctionsGraphing Exponential Functions

You TryIs this a growth or decay

function???

Translating FunctionsTranslating Functions

y = abx-h+k

Stretch / Shrink

NEGATIVE a =

reflection!!BASE

Will determine if growth or decay

HORIZONTAL SHIFT

(opposite direction)

VERTICAL SHIFT

Translating FunctionsTranslating Functions

Always graph y=abx first, then

translate the function!!

Domain/RangeDomain/Range

The DOMAIN is all real numbers

The RANGE is determined by the VERTICAL shift of the

graph!! Find the asymptote!!

HomeworkHomework

pg. 122: 1 – 9 all

AND

pg. 126: 1 – 9 all