Function in Maths

A function in math is like a machine that takes an input, does something to it, and gives a specific output. For each input, there’s exactly one output. It’s a rule that connects each input to one and only one result. Functions are fundamental in fields like algebra and calculus. They help model relationships and solve real-world problems.

Here is how we represent the function,

f(x) = y [Here, f() is a function, x is the input, and y is the corresponding output.]

If we collect, all inputs in one set that says "A" and collect all outputs in one set that says "B". then we can also write the function as,

f: A→B [This means that for every element x in set A, there is exactly one element f(x) in set B.]

For Example, consider the function f(x) = 2x. If the input is 3, the output is f(3) = 2 * 3 = 6. The function takes the value of x, performs an operation on it (in this case, multiplication by 2), and returns the result.

What is a Function in Maths?

In mathematics, a function is a relationship or rule that assigns each input (often called the domain) to exactly one output (often called the co-domain).

Key Concepts of Functions

This section introduces the core ideas of functions, including notation, domain, range, and real-life applications.

• Introduction to Functions
• Function Notation
• Domain and Range of a Function
• Classes of Functions
• Codomain vs. Range
• Real-Life Applications of Functions

Types of Functions

Learn about various types of functions based on their mapping, algebraic nature, and special behaviors like periodicity or symmetry.

• Based on Mapping Properties
  • One-to-One (Injective) Function
  • Onto (Surjective) Function
  • Bijective Function
  • Many-One Function

• Algebraic Functions
  • Constant Function
  • Identity Function
  • Polynomial Function
  • Rational Function
  • Linear Functions
  • Absolute Value Function

• Transcendental Functions
  • Exponential Function
  • Logarithmic Function
  • Trigonometric Function
  • Inverse Trigonometric Functions

• Special Categories
  • Piecewise Functions
  • Even and Odd Functions
  • Periodic Functions
  • Increasing and Decreasing Functions

• Real-World Functions
  • Real Functions
  • Real-Valued Functions
  • Implicit Functions

Operations on Functions

Understand how functions can be combined, composed, or inverted, along with algebraic operations on different kinds of functions.

• Algebra of Functions
  • Algebra of Derivative of Functions
  • Algebra of Real Functions
  • Algebra of Continuous Functions

• Advanced Operations
  • Algebra of Real Functions
  • Composition of Functions
  • Inverse of a Function
  • Vertical Line Test

Graphic Representation of Functions

Explore how functions are visualized using graphs and tables, and how to analyze the behavior of different function types graphically.

• What is a Function Table?
• Graphing of Function
• Graphing Quadratic Function
• Graphing Polynomial Functions
• Graphing Rational Function with Holes
• Graphing Sine and Cosine Functions
• Analyzing the Graphs of Functions

Practice Questions & Quizzes on Functions

Test your knowledge with practice problems, quizzes, and worksheets on functions and their properties.

• Practice Questions on Functions
• Quiz on Functions
• Quiz on Relation and Function
• Even and Odd Trigonometric Functions
• Domain and Range Worksheet

Conclusion

In Summary, Functions are the building blocks of mathematics, connecting inputs to outputs in predictable ways. Whether you're solving equations or modeling real-world phenomena, understanding functions is essential.