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(7.1 & 7.2) NOTES- Exponential Growth and Decay

(7.1 & 7.2) NOTES- Exponential Growth and Decay

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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

Text of (7.1 & 7.2) NOTES- Exponential Growth and Decay

Page 1: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

(7.1 & 7.2) NOTES- Exponential Growth and Decay

Page 2: (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)

Page 3: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

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

Page 4: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

3( ) 2xf x

Transformations:

Eq. of asymptote:

Domain:

Range:

Left 3

y = 0

x x

0y y

Page 5: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

2( ) 2 4xf x

Transformations:

Eq. of asymptote:

Domain:

Range:

Right 2, down 4

y = -4

x x

4y y

Page 6: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

( ) 2 3xf x

Transformations:

Eq. of asymptote:

Domain:

Range:

Reflect in x-axis, up 3

y = 3

x x

3y y

Page 7: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

2( ) 2 1xf x

Transformations:

Eq. of asymptote:

Domain:

Range:

Right 2, down 1

y = -1

x x

1y y

Page 8: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

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

Page 9: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

1'( ) 1

3

x

g x

Transformations:

Eq. of asymptote:

Domain:

Range:

Up 1

y = 1

x x

1y y

Page 10: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

1'( ) 3

3

x

g x

Transformations:

Eq. of asymptote:

Domain:

Range:

Down 3

y = -3

x x

3y y

Page 11: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

1'( )

3

x

g x

Transformations:

Eq. of asymptote:

Domain:

Range:

Reflect in x-axis

y = 0

x x

0y y

Page 12: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

1'( ) 2

3

x

g x

Transformations:

Eq. of asymptote:

Domain:

Range:

Reflect in x-axis, up 2

y = 2

x x

2y y

Page 13: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

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

Page 14: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

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

Page 15: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

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

Page 16: (7.1 & 7.2) NOTES- Exponential Growth                                     and Decay

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