Variation 3 · answer guide

Graph transformations — Reject reciprocal

Question

For , which statement about is true?

is even with asymptotes
has a zero where has a vertical asymptote
has a horizontal asymptote and is not the even graph shown in the original question
is identical to

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.As , , so .
Finish the calculation, then check that the result meets the question’s conditions.Reciprocal does not create the even pair of vertical asymptotes of .
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: Compare limiting heights: reciprocal , not the original asymptote pair.

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