Chapter 4 Topics – Functions and Graphs
Click on any topic to expand and view its exercises. Each section includes step-by-step solutions and real-world applications.
4.1 – Function Operations & Composition
Addition, subtraction, multiplication, division, composition of functions
New 2026
This section covers operations on functions including addition, subtraction, multiplication, division, and composition \((f \circ g)(x) = f(g(x))\). You'll learn to combine functions and find their domains.
4.1
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Exercise 4.1
Operations & composition of functions
4.2 – Absolute Value Functions & Graphs
Graphing absolute value functions, vertex, symmetry, solving absolute value equations
New 2026
This section introduces absolute value functions \(f(x) = |x - h| + k\) and their V-shaped graphs. You'll learn to find the vertex, axis of symmetry, and solve absolute value equations using the \(\pm\) property.
4.2
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Exercise 4.2
Absolute value graphs & equations
4.3 – Real-World Applications & Inequalities
Modeling real-world problems, absolute value inequalities
New 2026
This section applies functions and absolute value inequalities to real-world scenarios including business profit models, discount calculations, temperature tolerance, manufacturing precision, and GPS accuracy.
4.3
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Exercise 4.3
Applications & absolute value inequalities
Review Exercise 4
Complete revision and mixed practice problems
New 2026
The review exercise mixes questions from all sections of Chapter 4, including MCQs on function notation, composition, inverse functions, absolute value graphs, and real-world problem solving.
R
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Review Exercise 4
Complete Revision & Practice
Functions and Graphs – What's Inside This Chapter (PECTAA 2026)
Chapter 4 – Functions and Graphs is part of Class 10 Mathematics under the Revised National Curriculum 2023. Functions model relationships between variables. This unit covers various function types, their properties, graphing techniques, and applications in scientific research, data analysis, and modeling real-world phenomena.
Prepared by Muhammad Tayyab, Govt Christian High School Daska, this chapter's notes cover all 3 exercises plus the review exercise, with step-by-step solutions throughout.
✅ What This Chapter Covers
- ✓Function operations: addition, subtraction, multiplication, division
- ✓Composite functions and inverse functions
- ✓Absolute value functions and their V-shaped graphs
- ✓Solving absolute value equations and inequalities
- ✓Real-world applications in business, manufacturing, and science
🌐 Why This Chapter Matters
Functions model relationships between variables. This unit covers various function types, their properties, graphing techniques, and applications in scientific research, data analysis, and modeling real-world phenomena.
Mastering this chapter builds a foundation for higher studies and board exam success under the PECTAA 2026 syllabus.
Browse Notes by Individual Chapter
Each chapter also has its own dedicated page with exercise cards and full notes.
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Chapter 1: Complex Numbers
Complex number operations, Argand diagrams, and engineering applications with step-by-step solved exercises.
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Chapter 2: Quadratic Equations and Inequalities
Solving techniques, discriminant analysis, optimization applications, and real-world problem solving strategies.
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Chapter 3: Matrices and Determinants
Matrix operations, determinants, inverses, and computer graphics applications with complete solved exercises.
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Chapter 4: Functions and Graphs
Function types, properties, graphing techniques, and scientific applications for comprehensive understanding.
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Chapter 5: Algebraic Fractions
Simplification, operations, solving equations, and engineering applications with detailed step-by-step solutions.
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Chapter 6: Vectors in Plane
Vector operations, dot product, and physics and engineering applications with practical solved problems.
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Chapter 7: Trigonometry
Trigonometric identities, equations, inverse functions, and real-world applications in architecture and navigation.
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Chapter 8: Chords and Arcs of a Circle
Relationships between chords, arcs, angles, and design and engineering applications for circular geometry.
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Chapter 9: Tangent and Angles of a Circle
Tangent properties, angle relationships, and geometry and design applications with construction techniques.
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Chapter 10: Practical Geometry of Circles
Geometric constructions, tangents, inscribed figures, and step-by-step methods for technical drawing.
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Chapter 11: Information Handling
Data collection, graphical representations, statistical analysis, and decision making for real-world problems.
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Chapter 12: Probability
Basic concepts, compound events, conditional probability, and real-world applications in risk assessment.
Explore the Complete Class 10 Math Toolkit
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Class 10 Math Notes Hub
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Math Key Book
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Notes PDF
Downloadable and printable chapter-wise PDF notes for offline study.
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Solved Exercises
Step-by-step worked solutions for every exercise in all 12 chapters.
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Important Questions
Short and long board-focused questions to prioritize your revision.
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Math MCQs
Chapter-wise multiple-choice questions with an online practice test.
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Definitions
Every key term and theorem explained clearly, chapter by chapter.
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Formula Sheet
A quick-revision sheet with all formulas organized by chapter.
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Guess Paper
The latest important chapters and exercises predicted for this year's exam.
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Past Papers
Solved previous board papers with pattern analysis for smarter prep.