Q. 104 - Precalculus Enhanced with Graphing Utilities

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 $-1$.

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the reflection about $y$ axis

Step 2: Checking the translation

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

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 $g\left(x\right)=f\left(x\right)$