Variation 2 · answer guide

Graph transformations — Reflection only

Question

If has a single vertical asymptote at (and is not even), which of the following produces a graph with a single asymptote 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. maps the asymptote to and does not duplicate it.
Finish the calculation, then check that the result meets the question’s conditions. would give asymptotes at both .
Match the result to the choices and state the correct option.Therefore option C is correct.

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

Verification: A pure left–right reflection moves one asymptote without copying it.

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