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

Two basic trigonometric graphs are described. Graph A has range

[-1,1]

and is defined for all real

x.

Graph B has vertical asymptotes at

x=\frac{\pi}{2}+k\pi

and takes every real value.

Total: 4 marks

(a) Name one possible function for Graph A. (1 mark)

(b) Name the basic function that fits Graph B. (1 mark)

(d) Explain why Graph B cannot be $\sin x$ . (1 mark)

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

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