Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Compare two transformations of the same parent function
Problem
Compare \(g(x)=f(x)+3\) and \(h(x)=f(x-2)+3\) with parent \(f\).
Big Picture
What this problem is really about
Decode each transformed rule on its own before comparing them. Changes outside the function move outputs vertically, while changes inside the input move graph features horizontally with the opposite-sign convention. Mapping the same general parent point through both rules will make the shared movement and the extra movement easy to distinguish.
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