Common Functions

Some Common Function that commonly used in mathematics are discussed below:

Real Function

Real function in maths refers to a function whose domain and range are subsets of the real numbers (denoted as ℝ). In simpler terms, a real function is a mathematical rule or relationship that assigns a real number value to each real number input.

Real Functions

Polynomial Function

The function in which the exponents of algebraic variables are non-negative integers is called a Polynomial Function. If the power of the variable is 1 it is called a linear function, if the power is 2 it is called a quadratic function, and if the power is 3 it is called a cubic function. Some examples of polynomial functions are mentioned below:

y = x²
y = 2x + 3
y = 3x³

Polynomial Function can further classified into following types:

Linear function: Linear Function is those in which maximum power of variable is 1. The general Form of Linear Function is y = mx + c

Quadratic Function: Quadratic Function is those in which maximum power of variable is 2. General Form of quadratic function is, ax² + bx + c = 0

Cubic Function: Cubic Function is those in which maximum power of variable is 3. General Form of cubic function is given as ax³ + bx² + cx + d = 0

Inverse Function

Inverse Function is the function containing the inverse of another function. Let’s say we have a function y = f(x) then its inverse function will be x = f^-1(y). In y = f(x), the domain is x and the range is y while in the case of x = f^-1(y), the domain is y and the range is x. Thus we can say that the domain of the original function is the range of its inverse function and the range of the original function is the domain of the original function. Some examples of inverse functions are,

y = tan^-1(x)
y = x^-1

Area Function

Area function typically refers to a mathematical function that calculates the area of a geometric shape or region. The area function takes one or more parameters as input and returns the area of the corresponding shape. Some of the area functions are discussed below:

Area of Circle Function: Area of Circle (A) is a function of its radius(r) such that,

A = πr²

Area of Triangle Function: Area of Triangle (A) is a function of its base(b) and height(h) such that,

A = (bh)/2

Exponential Function

Exponential function is the one which is represented as f(x) = e^x. It is often used to show rapid growth or decay.

Logarithmic Function

Logarithmic function is a mathematical function that represents the inverse operation of exponentiation. It is represented as f(x) = log x.

Ceiling Function

Ceiling function, denoted as ⌈x⌉, rounds a real number x up to the nearest integer that is greater than or equal to x. In other words, it finds the smallest integer value that is greater than or equal to x.

Floor Function

Floor function, denoted as ⌊x⌋, rounds a real number x down to the nearest integer that is less than or equal to x. In other words, it finds the largest integer value that is less than or equal to x.

Modulus Function

Modulus function, also known as the absolute value function, returns the magnitude or “size” of a real number without regard to its sign. Modulus function is denoted as ∣x∣, where x is the input value.

Signum Function

Signum function, also known as the sign function or signum function, is a mathematical function that returns the sign of a real number. It indicates whether the number is positive, negative, or zero.

Trigonometric Functions

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot).

Complex Functions

Any function in which the input variable are complex function are called the complex function. A complex number is a number that can be plot on the complex plane. In a complex number we have real number and imaginary number. A complex number(z) is represented as, z= x + iy and a complex function is represented as, f(z) = P(x, y) + iQ(x, y)

What is a Function in Maths?

A Function in maths is a special relation between the set of input values and the set of output values. In Function, each input value gives a particular output value. We represent a function in maths as, y = f(x) where x is the input value and for each x we get an output value as y.

In this article, we will learn about, functions in mathematics, their various types, examples, and others in detail.

Table of Content

What is a Function in Maths?

Function Definition in Maths

Functions Examples
Condition for a Function
Representation of Functions in Math
Identification of Function
Types of Function
What is a Function in Algebra?

Domain and Range of a Function

Composition of Functions
Algebra of Functions
What is a Function on a Graph?

Graphing Functions

Common Functions
Applications of Functions
Examples on Function
Practice Problems on What is a Function