Answer
See graph
Work Step by Step
→ The function is even, i.e. $f(x) = f(-x)$. What it means for the graph is that it's symmetric with respect to y=axis.
→ $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} f(-x)=0 $
→ The y-intercept is $y=f(0)=e^{-0^2} = 1$
→ The function derivative $(-2xe^{-x^2})$ is positive for negative values of $x$, zero at $x=0$ and negative at positive values of $x$. Thus the graph rises from zero from the far left corner, rises up to 1 at x=0, and gradually approaches the x-axis again.
