## Absolute Value Function (Equation)

### The absolute value function is a mathematical function that returns the magnitude or distance of a number from zero

The absolute value function is a mathematical function that returns the magnitude or distance of a number from zero. It is denoted by the symbol “| |” surrounding the input number. The absolute value of a number can be considered as its “positive value” and it is always non-negative.

The general equation for the absolute value function is:

| x | = x, if x ≥ 0

| x | = -x, if x < 0
In other words, if the input number (x) is positive or zero, then the absolute value of x is equal to x itself. However, if x is negative, then the absolute value of x is equal to its negation or the opposite (-x).
Let's consider a few examples to understand this concept:
1. | 5 | = 5
Here, the input number (5) is positive, so the absolute value of 5 is 5 itself.
2. | -3 | = 3
In this case, the input number (-3) is negative, so the absolute value of -3 is its negation, which is 3.
3. | 0 | = 0
When the input number is zero, the absolute value is also zero since it is equidistant from positive and negative numbers.
The absolute value function is commonly used in various areas of mathematics, such as solving equations involving absolute values, finding the distance between two numbers on a number line, and representing functions that have both positive and negative values.

##### More Answers:

The Square Root Function | Understanding the Principal Square Root and its Mathematical RepresentationHow to Evaluate Limits in Mathematics | Four Effective Techniques Explained

Understanding Quadratic Functions | Exploring the Properties and Solutions of Polynomial Equations