Question

How do you graph `y=4^(x-2)-1`?

Answer 1

The graph of `y` is the standard exponential increasing graph of `f(x)= 4^x` scaled by `1/16` and shifted one unit negative ("down") on the `y-`axis.

Explanation:

`y=4^(x-2) -1`

We can rewrite `y` as: `y=4^x/4^2 -1`

`y= 1/16*4^x -1`

Consider the standard exponential increasing graph of `f(x)= 4^x` below.

graph{4^x [-10, 10, -5, 5]}

We can now see that the graph of `y` is the graph of `f(x)= 4^x` scaled by `1/16` and shifted one unit negative ("down") on the `y-`axis. As below:

graph{4^(x-2) -1 [-10, 10, -5, 5]}