Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Transform a function table using a given rule
Problem
Use the source table to construct the table for \(g(x)=f(x)+3\). Name the transformation, write its coordinate map, transform every ordered pair, identify the coordinate that remains unchanged, and verify \(g(0)\).
Because the change is outside f, it transforms outputs rather than input locations. We’ll write the vertical point map, keep every x-coordinate fixed, apply the output change to each source row, and verify the transformed value at zero directly from the function rule.
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