Understanding the Absolute Value Function | A Mathematical Guide

Absolute Value Function

The absolute value function, also known as the modulus function, is a mathematical function that returns the magnitude or distance of a number from zero on the number line

The absolute value function, also known as the modulus function, is a mathematical function that returns the magnitude or distance of a number from zero on the number line. It is denoted by the symbol |x|, where x can be any real number.

The absolute value function takes a real number as input and returns a non-negative value. The output is always positive or zero, regardless of the sign of the input.

Formally, the absolute value function is defined as follows:

For any real number x, the absolute value of x, denoted as |x|, is defined as:
– |x| = x, if x is greater than or equal to zero.
– |x| = -x, if x is less than zero.

In simpler terms, if the input of the absolute value function is a positive number or zero, then the output is the same as the input. If the input is a negative number, the function returns its positive equivalent (by negating the negative sign).

For example:
– |3| = 3 because 3 is greater than zero.
– |-5| = 5 because -5 is less than zero, so we negate the negative sign.

The absolute value function is often used to find the distance between two numbers or to express the magnitude of a quantity without considering its direction. It has various applications in mathematics, physics, and other fields.

More Answers: