BBE Mathematics Unit 1 and Chapter 2 Notes (DU - Maharaja Agrasen College): Functions, Graphs & Equations

Mathematics is one of the core foundations of the Bachelor of Business Economics (BBE) course. Whether you study microeconomics, macroeconomics, statistics, or econometrics later, mathematics is the language that helps you understand how variables behave, how markets respond, and how quantitative decisions are made. Unit 1 and Chapter 2 of the BBE Mathematics syllabus taught at Maharaja Agrasen College (Delhi University) focuses on essential topics that build conceptual clarity and analytical skills. These topics include functions of variables, graph of equations, equation of a circle, graph of functions, and the general linear equation in a plane.

In this 1200-word blog, we will break down each topic in a simple, student-friendly, and exam-oriented way. These notes are designed for quick revision, conceptual understanding, and supporting your mathematical foundation for further economics subjects.

1. Functions of Variables

A function is one of the most important concepts in mathematics and economics. A function shows the relationship between two or more variables. In economics, we study various functional relationships such as demand function, cost function, utility function, and production function.

Definition

A function is a rule that assigns every value of an independent variable (x) exactly one value of the dependent variable (y).

Written as:
y = f(x)

If a function has two independent variables, it is written as:
z = f(x, y)

Domain and Range

• Domain: All possible input values (x) for which a function is defined.

• Range: All possible output values (y) the function can produce.

Types of Functions

1. Linear Function – f(x) = ax + b

   • Straight line; constant rate of change

2. Quadratic Function – f(x) = ax² + bx + c

   • Parabolic curve; increasing or decreasing

3. Exponential Function – f(x) = a·bˣ

   • Used in growth/decay models

4. Logarithmic Function – f(x) = logₐ(x)

   • Used in elasticity and measurement

5. Rational Function – f(x) = p(x)/q(x)

   • Breaks at points where q(x) = 0

Importance in Economics

• Demand decreases when price increases → D = f(P)

• Cost increases with output → C = f(Q)

• Revenue depends on price × quantity → R = f(P, Q)

Understanding functions helps BBE students interpret economic behaviour mathematically.

2. Graph of Equations

Graphs are a visual tool for understanding the behaviour of mathematical and economic relationships. Graphs allow us to see the movement of variables, patterns, growth, decline, and interactions.

Linear Equations

A linear equation is of the form:
ax + by + c = 0

Graph: A straight line

Properties:

• Slope = –a/b

• Intercepts:

  • x-intercept = –c/a

  • y-intercept = –c/b

Quadratic Equations

y = ax² + bx + c
Graph: A parabola

• If a > 0 → opens upward

• If a < 0 → opens downward

• Vertex (turning point) shows minimum/maximum value

Why Graphs Are Important in Economics

• Demand curves show relationship between price and quantity

• Supply curves show producer behaviour

• Revenue and cost curves help study profit

• Equilibrium is determined where two graphs intersect

Graphs make complex data easy to interpret visually.

3. Equation of a Circle

The equation of a circle is one of the most fundamental topics in coordinate geometry.

Standard Form

The equation of a circle with centre (a, b) and radius r is:

(x – a)² + (y – b)² = r²

Example:
If centre = (2, 3) and radius = 4
Equation → (x – 2)² + (y – 3)² = 16

General Form

x² + y² + 2gx + 2fy + c = 0

Here,

• Centre = (–g, –f)

• Radius = √(g² + f² – c)

How to Convert General Form to Standard Form

Complete the square:

1. Group x and y terms

2. Complete square for each

3. Rearrange into standard form

Why a Circle Matters in Analytical Geometry

• Helps understand distance formula

• Useful in optimization problems

• Forms the basis of conic sections

Understanding circle equations prepares students for advanced geometric and economic modelling.

4. Graph of Functions

Graphing functions helps visualize how dependent variables change when independent variables change.

Types of Graphs

1. Increasing and Decreasing Functions

• If f(x₁) < f(x₂) for x₁ < x₂ → Increasing function

• If f(x₁) > f(x₂) → Decreasing function

2. Even and Odd Functions

• Even Function: f(–x) = f(x)

  • Symmetric around y-axis

• Odd Function: f(–x) = –f(x)

  • Symmetric around origin

3. Exponential Growth Curves

These rise rapidly and are common in population growth and compound interest.

4. Logarithmic Curves

These rise quickly initially and then slow down. Used in elasticity, utility, and measurement.

5. Polynomial Graphs

These show multiple turning points, depending on their degree.

Importance in Economics

• Demand curves are downward sloping

• Total cost curves rise with increasing output

• Marginal revenue curves slope downward

• Utility functions show diminishing returns

Graphs turn formulas into meaningful visual behaviour.

5. General Linear Equation in a Plane

The general linear equation in two-variable coordinate geometry is:

ax + by + c = 0

This form represents a straight line.

Forms of Linear Equation

1. Slope-Intercept Form

y = mx + c
Where m = slope, c = y-intercept.

2. Intercept Form

x/a + y/b = 0
Where a = x-intercept, b = y-intercept.

3. Point-Slope Form

y - y₁ = m(x - x₁)

Meaning of Slope

Slope (m) represents rate of change:

• Positive slope → line rises

• Negative slope → line falls

• Zero slope → horizontal line

• Undefined slope → vertical line

Economic Interpretation

Straight-line equations represent:

• Budget lines

• Supply curves

• Cost functions

• Profit lines

• Linear demand functions

A strong understanding of linear equations helps analyse all types of business and economic relationships.

Conclusion

Chapter 2 of BBE Mathematics is crucial because it prepares students for all future quantitative subjects in the BBE curriculum. Whether it's economics, statistics, econometrics, finance, or business analytics, the concepts of functions, graphs, circle equations, and linear equations appear everywhere.

These notes simplify the technical aspects and make learning easier for DU BBE students, especially those from Maharaja Agrasen College. With clear definitions, formulas, examples, and applications in economics, these Chapter 2 notes can help you revise quickly and perform better in exams.