Graph transformations — Sign and fixed points

Question

Suppose , , , and for near . List three features of .

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.Vertical asymptote at .
Finish the calculation, then check that the result meets the question’s conditions.The point remains fixed; remains fixed.
State the final answer clearly in the form the question requested.Immediately left of , is large positive.

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

Verification: Zeros asymptotes; fixed; signs preserved.

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