Class 9 Math Chapter 10: All Notes & Resources
Choose a resource below for Chapter 10 Graphs of Functions, from solved exercises to definitions and MCQs.
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Class 9 Mathematics Chapter 10 introduces the visual representation of functions through graphs. You will learn to plot linear, quadratic, cubic, reciprocal, and exponential functions, understand their key features, and use graphs to solve real-world problems involving growth, decay, and optimization. This hub gathers every Chapter 10 resource in one place. Start with the Chapter 10 definitions for quick revision, then move to the solved exercises below. For targeted practice, try the Chapter 10 MCQs. You can also review the Grade 9 Math Pairing Scheme to understand paper weightings. When you are done, return to the main Class 9 Mathematics page for the next chapter.
Last updated: October 23, 2026
Exercise 10.1 Solved
Sketch graphs of linear and quadratic functions, and plot cubic, reciprocal, and exponential functions using tables of values.
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Exercise 10.2 Solved
Apply exponential growth and decay models to real-world scenarios, and find the gradient of a curve by drawing tangents.
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Review Exercise 10
Comprehensive mixed problems covering the entire chapter, including multiple-choice questions and real-life applications of graphs.
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Chapter 10 Definitions
All key definitions and formulas for functions, linear, quadratic, cubic, reciprocal, and exponential graphs.
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Chapter 10 MCQs
Multiple-choice questions covering the entire chapter with detailed solutions, perfect for exam preparation and self-testing.
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Muhammad Tayyab
Subject Specialist Math
MSc Mathematics · Govt Christian High School Daska, Sialkot, Punjab
Last updated: October 23, 2026
Key Concepts – Graphs of Functions
Linear Function
\(y = mx + c\)
A straight-line graph where \(m\) is the slope and \(c\) is the y-intercept.
Quadratic Function
\(y = ax^2 + bx + c\)
The graph is a parabola that opens upward if \(a > 0\) and downward if \(a < 0\).
Cubic Function
\(y = ax^3 + bx^2 + cx + d\)
An S-shaped curve that can have at most two turning points.
Reciprocal Function
\(y = \frac{a}{x}\)
Has two branches and asymptotes at \(x = 0\) and \(y = 0\).
Exponential Function
\(y = ka^x\)
Represents growth (if \(a > 1\)) or decay (if \(0 < a < 1\)).
Gradient of a Curve
\(m = \frac{\Delta y}{\Delta x}\)
The gradient at a point on a curve is the slope of the tangent line at that point.
Chapter 10 Frequently Asked Questions
What is a function?
A function is a relationship between two variables where each input (independent variable) is associated with exactly one output (dependent variable). It is often written as \(y = f(x)\).
What is the shape of a quadratic function's graph?
The graph of a quadratic function is a parabola. If the coefficient of \(x^2\) is positive, it opens upward; if negative, it opens downward.
What is an exponential function?
An exponential function has the form \(y = ka^x\), where \(a > 0\) and \(a \neq 1\). It models growth when \(a > 1\) and decay when \(0 < a < 1\).
How do you find the gradient of a curve at a point?
The gradient of a curve at a point is found by drawing a tangent line to the curve at that point and then calculating the slope of the tangent line using two points on it.
What is the break-even point in business?
The break-even point is the number of units a business must sell to cover its total costs. It occurs where total revenue equals total cost. On a graph, it is the point where the revenue and cost lines intersect.
Created by Hira Science Academy | Aligned with Punjab Board 2027 Syllabus