Answer
To reflect the graph of the function about the y-axis, the $x$ values of the function are replaced with $-x$ in the function’s equation $f\left( x \right)$.
Work Step by Step
Consider the function $f$, having equation $y=f\left( x \right)$.
In a function, if we substitute x by –x, the values of the function obtained at x will now be obtained at –x and the corresponding values of y will remain the same.
The graph of the function that is reflected about the y-axis be $g$. Then, for the reflection about the y-axis, the y-coordinate of the reflected graph, $g$ , will remain the same as that of $f$ but the x-coordinates of $g$ will have exactly opposite values as the x-coordinates of $f$ , that is,
$\begin{align}
& x'=-x \\
& y'=y \\
\end{align}$
Thus, the x value of the function is to be replaced by –x for a reflection about the y-axis, that is,
$g\left( x \right)=f\left( -x \right)$
Hence, the points on the reflected graph about the y-axis will have points of the form $\left( -x,f\left( -x \right) \right)$.
