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A simple exponential function to graph is .
Notice that the graph has the -axis as an asymptote on the left, and increases very fast on the right.
Changing the base changes the shape of the graph.
Replacing with reflects the graph across the -axis; replacing with reflects it across the -axis.
Replacing with translates the graph units to the left.
Replacing with (which is the same as adding to the right side) translates the graph units up.
The function is the inverse function of . So, it is the reflection of that graph across the diagonal line .
When no base is written, assume that the log is base .