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C34

Page history last edited by PBworks 17 years, 2 months ago

Outcome: C34 demonstrate an understanding of how the parameter changes affect the graphs of exponential functions

 

Originator:  Stefan        (with f please)

 

Explanation:

The transformational form of exponential functions is:

 

 Formula

 

Depending what values you plug in where the graphs can vary completely.

Meaning of the Variables

VT    =    Vertical Translation

HT    =    Horizontal Translation

VS    =   Vertical Stretch

HS    =   Horizontal Stretch

 

To understand how everything affects the final graph here a little overview:

 

Vertical Translation

The VT represents the horizontal asymptote.

  >1 VT 0-1 VT positive VT negative VT 0-(-1) VT <-1 VT
VT asymptote = VT asymptote above x-axis asymptote below x-axis asymptote = VT

 

ex: VT of -3

Horizontal Translation

The HT shifts the graph to the left or right.

  >1 HT

0-1 HT

 

positive HT negative HT 0-(-1) HT <-1 HT
HT the bigger the value of the HT the more the graph shifts to the right the smaller the value of the HT the less the graph shifts to the right shifts to the right shifts to the left the smaller the value of the negative HT the less the graph shifts to the left the bigger the value of the negative HT the more the graph shifts to the left

ex:    blue=    HT of -3

         green= HT of 2

 

Vertical Stretch

The VS changes the y-intercept of the graph.

  >1 VS 0-1 VS positive VS negative VS 0-(-1) VS <-1 VS
VS the bigger the VS the bigger the value of the y-intercept the smaller the VS the smaller the value of the y-intercept no reflection reflection at the x-axis the smaller the negative VS the smaller the value of the y-intercept the bigger the negative VS the bigger the value of the y-intercept

 

ex:    blue=    VS of -2

       green=    VS of 3

Horizontal Stretch

The HS affects the slope of the exponential function graph.

 

>1 HS

0-1 HS

positive HS

negative HS

0-(-1) HS

<-1 HS

HS

the bigger the value the more flat the slope

the closer to 0 the steeper the slope

no reflection

reflection at the y-axis

the closer to 0 the steeper the slope

the bigger the value the more flat the slope

 ex:   blue =  HS of-2  

       green=  HS of 0.1


 

Sample Question:

State the changes the graph would have to the following function comparing to Formula without graphing it.

 

 

Formula

Changes:

VT =5

     =positive and bigger then 0

     = asymptote = VT=5

HS=positive and bigger than 1

    =the bigger the value the more flat the slope

HT=positive and bigger than 1

    =the bigger the value of the HT the more the graph shifts to the right

 

Summary: A graph with a asymptote of 5, a more flat slope than 2^x and a graph which is shift to the right.

 

Answer:

green= Formula   blue= Formula   

 

 


 Source: all examples created with http://www.e-tutor.com/et2/graphing

                all examples are with b=2

Comments (2)

Anonymous said

at 1:55 pm on Apr 28, 2007

.... took forever to understand and write -.-
going out for a run now!

Anonymous said

at 9:37 pm on Apr 29, 2007

Nice job Stefan. I think you might have columns in your explainations for VT and HT that your really don't need. It might make it less confusing to just use the changes that make a difference.

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