LESSON EIGHT: Graphing Logarithmic Functions
Recall that the LOG functions is the inverse of the EXPONENTIAL function.
To graph LOG functions, we first do a table of values for the EXPONENTIAL FUNCTION and then
INTERCHANGE the x- and y- values to create a table of values for the LOG FUNCTION.
Example: Graph
y  log 2 x
Method:
 Create a table of values at right for the
function

X
Y
-3
-2
-1
0.125 0.25 0.5
Table for
0
1
1
2
2
4
3
8
4 5
16 32
y  2x
y  2x
Interchange the x- and y- values, and graph
x
y
0.125 0.25 0.5
-3
-2
-1
Table for
1
0
2
1
4
2
y  log 2 x
Notice that the exponential graph doesn’t cross the x-axis, so the log graph doesn’t cross the y-axis.
8
3
16
4
32
5
Refer to the previous graph to fill in the table below.
y  log 2 x
y  2x
Domain
Range
x-intercept(s)
y-intercept(s)
Vertical Asymptote
Horizontal Asymptote
Intervals of Increase
Intervals of Decrease
Ex. Graph
X
y  log 3 x
-3
-2
-1
and fill in the table that follows. (Graph as many points as will fit.)
0
1
2
3
4
5
y
y  3x
X
y
-3
-2
y  log 3 x
-1
0
1
2
3
4
5
y  3x
Domain
Range
x-intercept(s)
y-intercept(s)
Vertical Asymptote
Horizontal Asymptote
Intervals of Increase
Intervals of Decrease
Hw. P.76 #11,12
y  log 3 x