Hi all, just looking at this function

$\displaystyle y = -e^{|-x-1|}+2 $

I have found the y-intercept to be $\displaystyle 2-e$ and x- intercepts to be $\displaystyle -1\pm\ln(2) $

These are correct.

I have also found a cusp type maximum at (-1,1) . Therefore $\displaystyle y \in (-\infty,1] $

This range was found using trial and error, is there a way to find this range other way for this type of function?