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Graphing Exponential and Logarithmic Functions

Graphing Exponential Functions

A simple exponential function to graph is y = 2 x .

x 3 2 1 0 1 2 3
y = 2 x 1 8 1 4 1 2 1 2 4 8

Math diagram

Notice that the graph has the x -axis as an asymptote on the left, and increases very fast on the right.

Changing the base changes the shape of the graph.

Math diagram

Replacing x with x reflects the graph across the y -axis; replacing y with y reflects it across the x -axis.

Math diagram

Replacing x with x + h translates the graph h units to the left.

Math diagram

Replacing y with y k (which is the same as adding k to the right side) translates the graph k units up.

Math diagram

Graphing Logarithmic Functions

The function y = log b x is the inverse function of y = b x . So, it is the reflection of that graph across the diagonal line y = x .

When no base is written, assume that the log is base 10 .

x 1 1000 1 100 1 10 1 10 100 1000
y = log x 3 2 1 0 1 2 3

Math diagram


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