Question

Reflection about the $x$-axis Open the reflection about the $x$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 the graph$f\left(x\right)=g\left(x\right)$

Step-by-step solution

Given information

Given the reflection about $y$axis

Checking the translation

Assume that $g\left(x\right)=f(ax)$

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

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

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