Graphing Logarithmic Functions
Example
Graph y = log2x.
Solution
| Step 1 Rewrite y = log2x in exponential form.
Step 2 Switch x and y.
Step 3 Calculate ordered pairs. |
x = 2y y = 2x |
|
x |
y = 2x |
(x, y) |
|
-4 |
 |
 |
|
-1 |
 |
 |
|
0 |
y = 20 = 1 |
(0, 1) |
|
1 |
y = 21 = 2 |
(1, 2) |
|
2 |
y = 22 = 4 |
(2, 4) |
|
4 |
y = 24 = 16 |
(4, 16) |
|
Step 4 Exchange the x- and y- coordinates.
The new coordinates are
(4, 2), and (16, 4).
Step 5 Graph the new ordered pairs.
Notice that the graph of y = log2x is the reflection about the
line y = x of y = 2x.
