Question

Reflection about the $y$-axis Open the reflection about the $y$axis applet. Move your mouse to grab the slider and change the value of $a$from $1$ to$-1$

Short answer

The function is the reflection of graph$g\left(x\right)=f\left(x\right)$

Step-by-step solution

Given information

Given the reflection about $y$axis

Checking the transformation

Assume that $g\left(x\right)=af\left(x\right)$

If the values of $a$changes from $1$to $-1$, then $g\left(x\right)=-f\left(x\right)$

Since $y=f\left(x\right)$and

$y=-f\left(x\right)$are equidistance from the $x$-axis, therefore $g\left(x\right)=-f\left(x\right)$is the reflection of the graph $g\left(x\right)=f\left(x\right)$