Find the graph of |y|=e−|x|−1
We will draw the graph of e−|x|−1 first and then do the transformation |y|=e−|x|−1. Our basic graph
is y=ex
(i) ex→e−x
(ii) e−x→e−x−1
(iii) e−x−1→e−|x|−1
We got the graph of y=e−|x|−1
To get |y|=e−|x|−1, we first drop the part below x-axis (∴|y|≥0).
But e−|x|−1 is always less than zero except at x=0. So the graph of |y|=e−|x|−1 will exist only at x=0.
So the graph will be just the point (0,0).