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Domain and Range Worksheet: Rational, Radical & Quadratic Functions + Key

Domain and Range Worksheet: Rational, Radical & Quadratic Functions + Key

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

10 August 2026

pdf, 117.38 KB
pdf, 117.38 KB

A worksheet on finding the domain and range of a function. The exercises include polynomial functions, rational functions and functions with square roots. Detailed solutions are included.

Master algebraic domain and range! A premium 9-page secondary maths resource featuring 18 domain problems, 9 advanced range tasks, and a complete 7-page step-by-step answer key.

Challenge your upper secondary and senior maths students with this rigorous Finding Domain and Range Worksheet: Rational & Radical Functions with Key. This 9-page packet focuses entirely on the algebraic analysis of function inputs and outputs. It provides the exact level of practice needed for A-Level, IB Mathematics, and Higher Tier GCSE students.

What’s Included:
• Page 1 (Domain): 18 algebraic problems focusing on zero denominators and negative square roots.
• Page 2 (Range): 9 complex problems requiring algebraic manipulation and boundary analysis.
• Pages 3–9 (Answer Key): 7 pages of complete, step-by-step worked solutions showing every line of working out.

Key Skills Practiced:
• Finding domain exclusions for cubic and quadratic denominators (e.g., x^3 - 8 = 0).
• Solving radical domain inequalities (e.g., x^2 - 5x >= 0).
• Determining range restrictions by isolating independent variables to find inverse limits.
• Finding quadratic range boundaries using turning points / vertex form.
• Expressing final answers clearly using correct set and interval notation.

Perfect For:
• Year 11 Higher GCSE, AS-Level, A-Level, and IB Math classes.
• Independent classroom learning logs or comprehensive homework packs.
• Rigorous exam preparation, revision sheets, and calculus readiness checks.

Get this resource as part of a bundle and save up to 65%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Functions Worksheet Bundle: Domain, Range, One-to-One & Inverses

A collection of three worksheets on the following topics: * Domain and Range of a Function:The exercises include polynomial functions, rational functions and functions with square roots. * Injective Functions: The exercises require to decide whether a function is injective or not given its equation or its graph. * Inverse Functions: The exercises require to decide whether a given function is invertible, find the inverse function and the domain of the inverse function. Detailed solutions are included. Simplify your advanced functions unit with this comprehensive, no-prep 3-worksheet bundle! Perfect for KS5, A-Level Maths, and Further Maths lessons, this print-and-go pack covers domain and range, injective functions, and finding inverse functions with full worked solutions included. ________________________________________ Looking for a rigorous, ready-to-print resource to help your sixth form students truly master functions? This complete 3-worksheet bundle takes students beyond basic equations to build deep conceptual fluency. From analyzing restricted domains to algebraically proving inverse relationships, this toolkit gives your A-Level Mathematics, Further Maths, or Advanced Extension Award classes the exact practice they need to tackle complex algebraic concepts with confidence. **What’s Included in This Bundle:** • Worksheet 1: Domain and Range – Features 18 rigorous problems covering linear, rational, radical, absolute value, and quadratic functions, alongside finding the range using interval notation. • Worksheet 2: Injective (One-to-One) Functions – Teaches students how to formally prove if a function is injective algebraically and visually using graphs and the horizontal line test. • Worksheet 3: Finding Inverse Functions – Guides students through verifying invertibility and finding inverses for advanced linear, quadratic, radical, rational, and piecewise functions. • Full Worked Solutions – Step-by-step, fully written mathematical solutions for every single problem to make marking effortless or facilitate student self-assessment! **Perfect For:** • Year 12 and Year 13 A-Level Mathematics (Pure Maths modules) • Further Maths & Advanced Extension Award (AEA) preparation • Independent Practice, Homework Tasks, or Cover Work • End-of-Unit Revision & Maths Intervention Groups **Curriculum Alignment:** Fully aligned with the UK National Curriculum for Advanced Level Mathematics and suitable for all major exam boards, including AQA, Edexcel, and OCR: • Algebra and Functions: Understand and use the definition of a function, including domain, range, one-to-one (injective) functions, and the restriction of domain to create invertible functions. • Inverse Functions: Find the inverse of a function, illustrate its graphical relationship to the original function, and understand the structural conditions for its existence. ________________________________________

£3.35
Bundle

Functions Worksheet Bundle | Domain, Range, Graphs, Even & Odd | Algebra 2

A collection of three worksheets on the following topics: * Identifying Graphs of Functions: identifying whether a given graph represents a function * Domain and Range of a Function: finding the domain and range of a function ( polynomial functions, rational functions and functions with square roots) * Even and Odd Functions Bundle: determining whether a function is even, odd or neither given its equation or graph. Detailed solutions are included. Master identifying functions, finding domain and range, and determining even and odd functions with this comprehensive math worksheet bundle! Complete with step-by-step solutions, this print-and-go resource is perfect for GCSE Higher, A-Level, and Core Maths students. Help your classes build conceptual mastery with both algebraic and graphical practice. ________________________________________ Are your students struggling to identify functions, calculate domain and range, or classify even and odd functions? This Functions Worksheet Bundle is the ultimate print-and-go solution to help your A-Level, Higher GCSE, or Key Stage 4/5 students build lasting algebraic and graphical confidence. This comprehensive math resource features clear layout graphics and step-by-step, fully worked solution sheets that take the guesswork out of grading, marking, or student self-checking! **What’s Included in This Bundle?** • **Identifying Graphs of Functions:** Coordinate plane graph practice utilizing the vertical line test to distinguish functions from non-functions. • **Domain and Range of a Function:** Extensive practice finding the domain of linear, quadratic, rational, and square root functions analytically. Includes finding the range of rational functions using algebraic manipulation. • **Even and Odd Functions:** Dual-focused practice where students determine if a function is even, odd, or neither using both algebraic proof calculations and graphical symmetry rules. • **Complete Step-by-Step Solutions:** Every single problem comes with a fully worked-out answer key, making this resource perfect for independent student work, homework assignments, or emergency cover lessons! **Why Teachers Love This Resource:** • No Prep Required: Simply download, print, and hand out to your classes immediately. • Scaffolded Learning: Exercises naturally progress from simple conceptual identification to multi-step rational and radical equations. • Versatile Classroom Use: Ideal for homework, classwork, revision booklets, retrieval practice, or end-of-topic assessments. • Clear, Clean Formatting: Designed with high-contrast, uncluttered visual layouts accessible to all learners. **Target Levels:** • Key Stage 4 (KS4) / GCSE Math: Excellent for Higher Tier students mastering function notation and graphs. • Key Stage 5 (KS5) / A-Level Mathematics: Perfect for the core pure mathematics modules covering coordinate geometry and algebraic functions.

£3.35

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