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 
01 VT 
positive VT 
negative VT 
0(1) VT 
<1 VT 
VT 
asymptote = VT 
asymptote above xaxis 
asymptote below xaxis 
asymptote = VT 
ex: VT of 3
The HT shifts the graph to the left or right.

>1 HT 
01 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 yintercept of the graph.

>1 VS 
01 VS 
positive VS 
negative VS 
0(1) VS 
<1 VS 
VS 
the bigger the VS the bigger the value of the yintercept 
the smaller the VS the smaller the value of the yintercept 
no reflection 
reflection at the xaxis 
the smaller the negative VS the smaller the value of the yintercept 
the bigger the negative VS the bigger the value of the yintercept 
ex: blue= VS of 2
green= VS of 3
Horizontal Stretch
The HS affects the slope of the exponential function graph.

>1 HS

01 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 yaxis

the closer to 0 the steeper the slope

the bigger the value the more flat the slope

ex: blue = HS of2
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.etutor.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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