DATE TEACHER NAME
The graph of $y=|x+4|-8$ is reflected across the $y$-axis.
What is an equation of the reflected graph? What is the name of the parent function?
a system of equations to represent the information. Identif
\(\boxed{y=|-x+4|-8}\) is the equation of the reflected graph and its parent function is \(\boxed{y=|x|}\).
Step 1 :The graph of \(y=|x+4|-8\) is reflected across the y-axis.
Step 2 :To reflect a graph across the y-axis, we replace \(x\) with \(-x\) in the equation.
Step 3 :So, the equation of the reflected graph is \(y=|-x+4|-8\).
Step 4 :The parent function of \(y=|x+4|-8\) is \(y=|x|\). This is because the graph of \(y=|x+4|-8\) is a transformation of the graph of \(y=|x|\), specifically, it is the graph of \(y=|x|\) shifted 4 units to the left and 8 units down.
Step 5 :So, the parent function of the reflected graph \(y=|-x+4|-8\) is also \(y=|x|\).
Step 6 :\(\boxed{y=|-x+4|-8}\) is the equation of the reflected graph and its parent function is \(\boxed{y=|x|}\).