Variation 3 · answer guide

Inverse trigonometric functions — Reciprocal distractor

Question

From to , the vertical dilation factor is

This practice question was inspired by Question 5 in the 2024 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: use the restricted domain and range that make the inverse function single-valued.The coefficient multiplies the function values: vertical factor .
Finish the calculation, then check that the result meets the question’s conditions.The affects only the horizontal scale ().
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: At large , range approaches rather than .

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