Connect the ideas.
- Check the original domain before simplifying.
- Composition acts from inner to outer.
- Injectivity depends on the chosen domain.
- Inverse functions exchange domain and range.
- Distinguish input transformations from output transformations.
- Use exact intercepts, holes, poles, derivatives and limits to organise each graph branch.
Put it together.
Choose a paper and show your working.
Functions and graph sketching — Practice test 1
Ten multipart questions combining exact calculations, domains, graph evidence, interpretation and reasoning. Show working and label key graph features.
10 questions · 46 marks · 70 minutes · Scientific calculatorFunctions and graph sketching — Practice test 2
Ten multipart questions combining exact calculations, domains, graph evidence, interpretation and reasoning. Show working and label key graph features.
10 questions · 48 marks · 70 minutes · Scientific calculatorFunctions and graph sketching — Practice test 3
Ten multipart questions combining exact calculations, domains, graph evidence, interpretation and reasoning. Show working and label key graph features.
10 questions · 49 marks · 70 minutes · Scientific calculatorFunctions and graph sketching — Practice test 4
Ten multipart questions combining exact calculations, domains, graph evidence, interpretation and reasoning. Show working and label key graph features.
10 questions · 48 marks · 70 minutes · Scientific calculatorFunctions and graph sketching — Practice test 5
Ten multipart questions combining exact calculations, domains, graph evidence, interpretation and reasoning. Show working and label key graph features.
10 questions · 51 marks · 70 minutes · Scientific calculatorFunctions and graph sketching — Practice test 6
Ten multipart questions combining exact calculations, domains, graph evidence, interpretation and reasoning. Show working and label key graph features.
10 questions · 50 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 Specialist functions and sketching graphs. Calculus-based analysis assumes concurrent Methods differentiation; real-polynomial division detail is taught in the separate Real Polynomials chapter.
Official curriculum source ↗