Worked ExamplesYear 12Level 3 · ChallengeHSCVCE

Free Year 12 HSC/VCE-style Functions and Graphs Practice with Worked Solutions

Ten exam-style questions on functions and their graphs: function notation, domain and range, transformations of points, composite and inverse functions, odd and even functions, and the key features of parabolas, hyperbolas and exponential curves. Every question has marks allocated and a complete step-by-step solution so students can check each line of their working.

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Year: Year 12
Subject: Mathematics
Topic: Functions
Difficulty: Level 3 · Challenge
Estimated time: 30 minutes
Curriculum: Australian Curriculum
Questions: 10
Answers: Included, with working
Format: PDF (A4) + print

Students will practise

evaluating functions and finding the natural domain and range
applying transformations to points and equations
forming composite functions and finding inverse functions
identifying intercepts, asymptotes, turning points and range for parabolas, hyperbolas and exponentials

Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: HSC/VCE-style Functions and Graphs Practice with Worked Solutions

You've reached the end of this topic — next up: Calculus

Study guide

How to use this worked examples

Print the PDF or complete it on screen. Write the student's name and date at the top.
Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
Record the score, celebrate what went well, then follow the "What's next" suggestion.

Common questions

Who is this worked examples for?

Year 12 students (typically ages 17–18) working on functions. It is pitched at level 3 · challenge.

Are the answers included?

Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.

How long does it take?

About 30 minutes for 10 questions. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Move on to Calculus.

Year 12 · Mathematics · Functions

HSC/VCE-style Functions and Graphs Practice with Worked Solutions

Success Tutoring

Student name:

Date:

Score: /

Answer every question, showing all working. Marks are shown in brackets. Total: 31 marks.

Section A: Notation, domain, range and transformations

1.f(x) = x² − 2x. Find f(3) and f(−1).[2 marks]

2.State the natural domain and the range of f(x) = √(2x − 6).[2 marks]

3.g(x) = . State the natural domain of g, and find g(0).[3 marks]

4.The point (1, 4) lies on the graph of y = f(x). Find the coordinates of its image on (a) y = 2f(x − 3) + 1 and (b) y = f(−x).[3 marks]

Section B: Composite, inverse, odd and even functions

5.f(x) = 2x + 1 and g(x) = x². Find (a) f(g(x)), (b) g(f(x)) and (c) f(g(2)).[3 marks]

6.f(x) = , x ≠ 2. Find the inverse function f⁻¹(x) and state its domain.[3 marks]

7.Determine whether each function is even, odd or neither: (a) f(x) = x³ − 4x, (b) g(x) = x⁴ + 2x², (c) h(x) = x² + x.[3 marks]

Section C: Key features of graphs

8.For the parabola y = (x − 2)² − 9, find the vertex, the y-intercept, the x-intercepts and the range.[4 marks]

9.For the hyperbola y = − 3, state the equations of the asymptotes and find the coordinates of the intercepts with the axes.[4 marks]

10.For the curve y = 2^x − 8, find the y-intercept, the x-intercept, the equation of the horizontal asymptote and the range.[4 marks]

Preview — the PDF contains the full resource and answer sheet.

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About this resource

Created by: Success Tutoring
Last reviewed: 1 October 2026
How it was made: Written by our team

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