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One-to-One (Injective) Functions Worksheet | Horizontal Line 91¶¶Òõt PreCalculus

One-to-One (Injective) Functions Worksheet | Horizontal Line 91¶¶Òõt PreCalculus

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

11 August 2026

pdf, 175.76 KB
pdf, 175.76 KB

Master one-to-one functions and injective functions with this rigorous, ready-to-print pure maths worksheet! Perfect for A-Level Maths, KS5, and IB Mathematics students, this resource includes fully worked step-by-step solutions to save you valuable marking time.

Help your secondary and college maths students achieve conceptual mastery over functional mappings with this no-prep One-to-One (Injective) Functions Worksheet! This resource is specifically engineered to bridge the gap between abstract algebraic proofs and visual graph analysis, providing a comprehensive review of function behavior.
With 12 multi-step, rigorous problems, this printable activity targets the exact depth required for upper-level secondary maths, sixth-form colleges, and introductory higher education courses. Students will practice proving injectivity algebraically before transitioning to visual coordinate grids to apply the horizontal line test across a wide variety of functions.

What’s Included in This Resource?
• Algebraic Proof Section: Questions requiring formal algebraic manipulation to verify if f(x1) = f(x2) implies x1 = x2 (including linear, cubic fractions, and radical bounds).
• Visual Graph Analysis: Multiple coordinate grids featuring a rich variety of functions—such as absolute value, reciprocal fractions, cosines, cubics, and exponentials—where students must apply the Horizontal Line 91¶¶Òõt.
• Fully Worked Solutions: Step-by-step mathematical answers for every single problem to make marking or student self-checking effortless.

Core Skills Covered:
• Proving if a function is injective (one-to-one) using algebraic definitions.
• Applying the Horizontal Line 91¶¶Òõt to determine map uniqueness visually.
• Recognizing how domain restrictions impact whether a function is one-to-one.
• Factoring challenging equations (such as sum/difference of cubes formulas) to determine real solution states.
• Evaluating trigonometric, exponential, radical, and rational parent functions.

Perfect For:
• AS & A-Level Mathematics (Pure Maths specifications)
• Key Stage 5 (KS5) / Sixth Form College
• GCSE Further / Additional Mathematics Extension
• International Baccalaureate (IB) Maths Higher Level (HL)
• Rigorous Homework, Exam Revision, Extension Work, or Cover Plans

Exam Board Alignment:
• Excellent preparation for Edexcel, AQA, OCR, and Cambridge International (CIE) specifications covering functions, domains, ranges, and injective mappings.

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

PreCalculus Functions Bundle | Composite, Inverse, Even Odd Worksheet Pack

A collection of 8 worksheets on functions. The following topics are included: * Identifying Graphs of Functions * Identifying Functions, Domain and Range-Set of Ordered Pairs * Evaluating Functions * Even and Odd Functions * Equality of Functions * Composition of Functions * Injective Functions * Inverse Functions (harder) Solutions are provided. Master advanced function mechanics with this complete A-Level Maths worksheet bundle! Perfectly optimized for Year 12 and Year 13 Pure Mathematics revision, this print-and-go pack covers composite functions, inverse proofs, odd/even functions, and piecewise evaluation with full step-by-step worked solutions. Looking for a rigorous, print-and-go resource pack to help your sixth-form students confidently master advanced functions? This Advanced Functions Mastery Worksheet Bundle contains a highly structured collection of problems designed to build fluency and deep analytical confidence. Moving from foundational index and mapping rules to tricky rational composition domains and formal inverse function derivations, this resource is perfect for daily secondary lessons, independent revision booklets, structured homework assignments, cover work, or university preparation! Every question includes an uncrowded, student-friendly layout and comes accompanied by a complete, step-by-step worked answer key making marking quick and straightforward for busy teachers or peer assessment. **What's Included in This Bundle?** • **Even and Odd Functions:** Fluency practice using algebraic substitutions and graphical charts to classify function symmetry. • **Equality of Functions:** Analyzing subset conditions to establish where two algebraic relationships match. • **Composition of Functions:** Extensive practice calculating composite functions alongside tracking rigorous domain conditions. • **Injective Functions:** Applying formal one-to-one definitions and horizontal graph checks. • **Inverse Functions:** Proving invertibility and rearranging equations to isolate the inverse function for rational, radical, and piecewise curves. • **Evaluating Functions:** Traditional calculation practice including nested parameters and multi-step piecewise functions. **Perfect For:** • AS & A-Level Mathematics: Targeted Pure Maths practice for Year 12 and Year 13 students pushing for maximum marks (Grades A and A*). • Advanced Higher / IB Diploma: Rigorous algebraic training for upper-level secondary curriculum paths. • Cover Work & Extensions: Self-contained layouts requiring zero prep work from you or a supply teacher.

£7.95
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

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