Question

Find the graph of $|y|=e^{-|x|}-1$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We will draw the graph of $e^{-|x|}-1$ first and then do the transformation $|y|=e^{-|x|}-1$. Our basic graph

is $y=e^x$

(i) $e^x\to e^{-x}$

(ii) $e^{-x}\to e^{-x}-1$

(iii) $e^{-x}-1\to e^{-|x|}-1$

We got the graph of $y=e^{-|x|}-1$

To get $|y|=e^{-|x|}-1$, we first drop the part below x-axis $(\therefore |y|\ge 0)$.

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).