Exponential and Logarithmic Transformations
Today we are going to explore the different components of exponential and logarithmic
functions and determine what each piece does to transform the original function. Please highlight
the function type your group is working on. Then visit one of the following sites.
f (x)  aBb(x c )  d or f (x)  a log B (b(x  c))  d
http://www.analyzemath.com/expfunction/expfunction.html
or
http://www.analyzemath.com/logfunction/logfunction.html

Take a couple minutes to play with the bars and see how the applet works. If you have any
questions about how to perform an operation please ask.
Now we are going to determine what each value does to the parent (original function).
x
Each group will start with B=2 ( f (x)  2 or f (x)  log 2 x ). Using one number at a time,
see if you can determine what a, b, c, and d do to your function.
In your own words please describe what you think the corresponding variables do to the
original function. 
a:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
b:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
c:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
d:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Once you have completed this, check with your teacher to make sure that you understand what
each value is supposed to do. When your teacher is okay with your responses, pick 2 people to
stay and teach, and 2 people to go and learn.
Which function are you learning about?
f (x)  aBb(x c )  d or f (x)  a log B (b(x  c))  d
What do the different values do to this function?

a:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
b:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
c:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
d:_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Go back to your groups and share out. Help your other group members learn and understand this
function.
REFLECTION:
1) Which values transform the functions the same way? Why do you think that is?
2) Which values transform in similar ways? Why do think that is?
3) State what you think each value will do to transform the given functions. Then use the applet
to check your answers.
a.
f (x)  3x transforms to
b.
g(x)  2  33(x 1)  4

g(x)  2  21(x 3)  1

c.
f (x)  (1 2) x transforms to
g(x)  2  (1 2)
3(x 1)
d.
1

f (x)  3x transforms to
g(x)  (1 2)  32(x 3)  2

e.
f (x)  log 3 x transforms to
f.
g(x)  2 log 3 (3(x  1))  4

f (x)  log 2 x transforms to
g(x)  log 2 (2(x  3))  1

f (x)  log 1 x transforms to
g.
2
h.
g(x)  2 log 1 (3(x 1)) 1
2

f (x)  2 x transforms to

f (x)  log 3 x transforms to
g(x)  (1 2) log 3 (2(x  3))  1