Question

complete this assessment to review what youve learned. it will not count toward your grade. a function and its reflection can be identified by the following equations: $f(x)=x - 2$ and $f(x)=-2 - x$. determine the line of reflection. enter the option number of your answer. option #1: the x - axis option #2: the y - axis option #3: $y = x$ option #4: $y=-x$ (1 point)

Explanation:

Step1: Recall reflection rules

Reflection over x - axis changes \(y\) to \(-y\), over y - axis changes \(x\) to \(-x\), over \(y = x\) swaps \(x\) and \(y\), over \(y=-x\) swaps \(x\) and \(y\) and changes their signs.
Let's take a general point \((x,y)\) on \(y = f(x)=x - 2\), so \(y=x - 2\).

Step2: Check reflection over \(y=-x\)

If we reflect a point \((x,y)\) over \(y=-x\), the transformation is \((x,y)\to(-y,-x)\).
For \(y=x - 2\), solve for \(x\) in terms of \(y\): \(x=y + 2\).
After reflection over \(y=-x\), the new \(x'=-y\) and new \(y'=-x\). Substituting \(x=y + 2\) into the reflection, we get \(y'=-(y' + 2)\), or \(y'=-2 - x'\).

Answer:

Option #4: \(y=-x\)