## Calculus, 10th Edition (Anton)

A function is an even function if and only if $f(-x)=f(x)$. For a function $g(x)$ to be symmetric about the y-axis, $g(x)$ and $g(-x)$ must have the same value or in other words, $g(x)=g(-x)$. This is clearly true from the definition of an even function.