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

1 Answer
Dec 20, 2017

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]}