exponential growth and decay functions. what is an exponential function? an exponential function has...

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