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← 2022 HSC Extension 1 paper Question 4

Variation 2 · answer guide

Graph transformations — Cancel opposing linear pieces

Question

If and , the sum graph is

  1. the horizontal line
  2. the line
  3. the line
  4. the parabola

This practice question was inspired by Question 4 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.

Step by step

  1. Set up the solution: track how each transformation moves key points, asymptotes and intercepts of the base graph..
  2. Finish the calculation, then check that the result meets the question’s conditions.A constant sum is a horizontal line.
  3. 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: Linear terms cancel; constants add.

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

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