Variation 1 · answer guide

Graph transformations — Absolute-value input

Question

Starting from a non-even graph defined for with a vertical asymptote at , which transformation produces an even graph with asymptotes at ?

This practice question was inspired by Question 2 in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: track how each transformation moves key points, asymptotes and intercepts of the base graph. copies the graph to , creating -axis symmetry and asymptotes .
Finish the calculation, then check that the result meets the question’s conditions. reflects below the -axis only; reflects left–right once; flips vertically.
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Even symmetry from a right-hand branch is the input map.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.