FRQ — Sets and Functions

Case study·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

Let

p(x)=x,\ q(x)=|x|,

and

r(x)=\operatorname{sgn}(x)

on the domain

\{-2,0,3\}.

Total: 4 marks

(a) Compare $p(-2)$ , $q(-2)$ , and $r(-2)$ . (1 mark)

(b) Compare $q(0)$ and $r(0)$ . (1 mark)

(d) A learner claims that $p$ and $q$ have the same range on this domain. Decide whether the claim is correct, and justify. (1 mark)

Your response (optional — you can also work on paper)

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