Variation 2 · answer guide

Inverse function — Absolute value creates extra level sets

Question

Starting from a cubic that dips below , the transformation most likely to create extra intersections with is

This practice question was inspired by Question 9 in the 2023 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: replace the function value by y, swap x and y, then solve for y.Reflecting negative parts upward can turn previously below-axis arcs into additional positive humps that the line can cross.
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: Same mechanism as the 2023 paper option D.

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