Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Write a transformed function from a verbal transformation description
Problem
Write the transformed function \(g(x)\) after shifting the parent \(f(x)\) right \(4~\text{units}\) and up \(2~\text{units}\).
Big Picture
What this problem is really about
Treat the two movements separately before combining them. Horizontal changes belong inside the function’s input and use the sign opposite the graph’s motion, while vertical changes are applied outside to every output. We’ll then check the completed rule by tracking how a general point on the parent graph moves.
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