Q. 103 - Precalculus Enhanced with Graphing Utilities

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 $-1$

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the reflection about $y$ axis

Step 2: Checking the transformation

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

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 $g\left(x\right)=f\left(x\right)$