MA160 - Section 3.2 Logarithmic Functions
Problem 1: 1) Construct a table of values for the function
f ( x)  2 x
2) Plot the ordered pairs and graph the function.
3) Use the ordered pairs from f(x) to construct the table for the inverse function and graph on the same coordinate system.
We do not know the formula for the inverse function.
x
y  f ( x)  2 x
x
y  f 1 ( x)
-2
-1
0
1
2
4) Complete the following, the left column is review. The right column can be answered by looking at graph of y  f 1 ( x)
For the exponential function
f ( x)  2 x
Domain
For the inverse function
Domain
Range
Range
x-intercept
x-intercept
y-intercept
y-intercept
asymptote
Asymptote
Increasing or decreasing?
Increasing or decreasing?
1
Problem 2: 1) Construct a table of values for the function
f ( x)  (1/ 2) x
2) Plot the ordered pairs and graph the function .
3) Use the ordered pairs from f(x) to construct the table for the inverse function and graph on the same coordinate system.
We do not know the formula for the inverse function.
x
y  f ( x)  (1/ 2) x
x
y  f 1 ( x)  .............
-2
-1
0
1
2
4) Complete the table. The left column is review; the right column can be answered by looking at the graph of y  f 1 ( x)
For the exponential function
f ( x)  (1/ 2) x
Domain
For the inverse function
Domain
Range
Range
x-intercept
x-intercept
y-intercept
y-intercept
asymptote
Asymptote
Increasing or decreasing?
Increasing or decreasing?
2
1.
How are exponential functions and logarithmic functions related?
2.
Write the definition of a logarithm.
3.
Write in exponential form
a.
log 2 16  4
c.
log5 625  4
b.
log 13 9  2
d.
log 8 2 
1
3
3
4.
Find each of the following logs
a.
log3 9 
b.
log3 81 
c.
log5 125 
d.
log 12 32 
e.
log 7
1

49
f.
log 2 128 
5.
What is a common log?
6.
What do we mean by log100 ?
4