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(7.1 & 7.2) NOTES- Exponential Growth and Decay. Definition : Consider the exponential function:. if 0 < a < 1 : exponential decay if a > 1: exponential growth. Asymptote:. A line that a graph approaches, but never reaches (boundary line). - PowerPoint PPT Presentation
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(7.1 & 7.2) NOTES- Exponential Growth and Decay
Definition: Consider the exponential function:
( ) xf x Ca
if 0 < a < 1: exponential decayif a > 1: exponential growth
Asymptote: A line that a graph approaches, but never reaches (boundary line)
Ex: Graph the given exponential function using a table and identifying the following: x y( ) 2xf x
a=______ C= ______(circle one) exponential decay or growthy- intercept: _________equation of asymptote: __________
d: __________ r: _____________
-2
-101
2
1/4
1/212
4
2 1
1( ) xf x Ca
y = 0
x x 0y y
3( ) 2xf x
Transformations:
Eq. of asymptote:
Domain:
Range:
Left 3
y = 0
x x
0y y
2( ) 2 4xf x
Transformations:
Eq. of asymptote:
Domain:
Range:
Right 2, down 4
y = -4
x x
4y y
( ) 2 3xf x
Transformations:
Eq. of asymptote:
Domain:
Range:
Reflect in x-axis, up 3
y = 3
x x
3y y
2( ) 2 1xf x
Transformations:
Eq. of asymptote:
Domain:
Range:
Right 2, down 1
y = -1
x x
1y y
Ex: Graph the given exponential function using an x/y-chart and identify the following: x y
a=______ C= ______(circle one) exponential decay or growthy- intercept: _________equation of asymptote: __________
d: __________ r: _____________
-2
-101
2
9
31
1/3
1/9
1/3 1
1( ) xf x Ca
y = 0
x x 0y y
1( )
3
x
g x
1'( ) 1
3
x
g x
Transformations:
Eq. of asymptote:
Domain:
Range:
Up 1
y = 1
x x
1y y
1'( ) 3
3
x
g x
Transformations:
Eq. of asymptote:
Domain:
Range:
Down 3
y = -3
x x
3y y
1'( )
3
x
g x
Transformations:
Eq. of asymptote:
Domain:
Range:
Reflect in x-axis
y = 0
x x
0y y
1'( ) 2
3
x
g x
Transformations:
Eq. of asymptote:
Domain:
Range:
Reflect in x-axis, up 2
y = 2
x x
2y y
Consider the parent equation, and
transformed equation
IN GENERAL, the following transform the graph of by:
h shifts: _______________
k shifts: _______________
reflects: _______________
Left or right
Up or down
x-axis
( ) xf x Ca
( ) .x hf x Ca k
f to f
equation of parent graph: ___________ a=_____ C= _____(circle one) exponential decay or growthtransformations: _______________________y-intercept: ____________equation of asymptote: _________________domain: _______________ range: _______________
Ex: Graph the exponential function: 1( ) 4 3xf x
x y-2
-101
2
1/16
1/414
16
( ) 4xf x 4 1
Left 1, down 31
y = -3 x x 3y y
( ) 4xf x
equation of parent graph: ___________ a=_____ C= _____(circle one) exponential decay or growthtransformations: _____________________________________y-intercept: ____________equation of asymptote: _________________domain: _______________ range: _______________
Ex: Graph the exponential function: 2
1( ) 5
4
x
f x
x y-2
-101
2
16
41
1/4
1/161
( )4
x
f x 1/4 -1
Reflect x-axis, right 2, up 5
1( )
4
x
f x
equation of parent graph: ___________ a=_____ C= _____(circle one) exponential decay or growthtransformations: _____________________________________y-intercept: ____________equation of asymptote: _________________domain: _______________ range: _______________
Ex: Graph the exponential function: 2
1( ) 5
4
x
f x
x y-2
-101
2
16
41
1/4
1/161
( )4
x
f x 1/4 -1
Reflect x-axis, right 2, up 5-11
y = 5 x x 5y y
1( )
4
x
f x
