Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Identify the horizontal shift of a quadratic or absolute-value function
Problem
Identify the horizontal shift from parent function \(f(x)=x^2\) to transformed function \(g(x)=(x-4)^2\).
Big Picture
What this problem is really about
A change inside the input creates a horizontal shift whose direction is opposite the visible sign. We’ll match the rule with f of x minus h, solve the correspondence between parent and transformed inputs, and track the vertex to confirm the direction and distance.
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