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Worked Examples12th GradeLevel 3 · Challenge

Free 12th Grade Senior 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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Grade
12th Grade
Subject
Math
Topic
Functions
Difficulty
Level 3 · Challenge
Estimated time
30 minutes
Curriculum
Texas grade levels (TEKS)
Questions
10
Answers
Included, with working
Format
PDF (A4) + print

Students will practice

  • 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: Texas grade levels (TEKS). We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Senior Functions and Graphs Practice with Worked Solutions

  1. 112th Grade Function Notation, Composites and Inverses Worksheet — Level 1
  2. 212th Grade Function Notation, Composites and Inverses Worksheet — Level 2
  3. 312th Grade Function Notation, Composites and Inverses Worksheet — Level 3
Study guide

How to use this worked examples

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

Common questions

Who is this worked examples for?

12th Grade 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?

Try 12th Grade Function Notation, Composites and Inverses Worksheet — Level 1.

Preview

Success TutoringWorksheets12th Grade · Mathematics · Functions

Senior Functions and Graphs Practice with Worked Solutions

Name

Date

Score /

Answer every question, showing all working. Marks are shown in parentheses. 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 = 2x − 8, find the y-intercept, the x-intercept, the equation of the horizontal asymptote and the range.[4 marks]
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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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