TestMum
← 2023 HSC Extension 1 paper Question 8

Variation 3 · answer guide

Graph transformations — Outer absolute value reflection

Question

Compared with , the graph of is obtained by

  1. reflecting the negative parts of in the -axis
  2. shifting unit right
  3. reflecting in the -axis only
  4. removing the absolute values

This practice question was inspired by Question 8 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.

Step by step

  1. Set up the solution: track how each transformation moves key points, asymptotes and intercepts of the base graph.Taking absolute value of an expression reflects any portion below the -axis above it.
  2. Finish the calculation, then check that the result meets the question’s conditions. is negative for ; those arms flip up under the outer modulus.
  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: For , .

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

← Back to 2023 HSC Extension 1 paper Question 8