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:
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
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 
without graphing it.
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= blue= 
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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