Graph transformations — From table to reciprocal

Question

A function satisfies , , , a local min. Sketch reasoning for near these values.

This practice question was inspired by Question 11(c) in the 2020 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.Asymptotes .
Finish the calculation, then check that the result meets the question’s conditions.At , , a local max if has a negative local min.
State the final answer clearly in the form the question requested.Between the asymptotes is negative, so is negative.

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

Verification: Matches the same reciprocal rules as the original sketch question.

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