Math Homework. Do It Faster, Learn It Better.

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

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.

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

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

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