Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Determine the effect of replacing \(x\) with \(-x\) in a function rule
Problem
Determine whether \(g(x)=f(-x)=(-x)^2\) is the reflection of the parent function \(f(x)=x^2\) across the \(y\text{-}\text{axis}\).
Big Picture
What this problem is really about
Replacing x with negative x changes inputs before the parent rule is evaluated, but the visible result depends on the parent’s symmetry. We’ll simplify the transformed rule with the parentheses intact, compare f of negative x with f of x, and use the point mapping and even-function test to determine both the reflection and whether the graph changes visibly.
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