## absolute value function

### The absolute value function, denoted as |x|, is a mathematical function that returns the non-negative value of a number

The absolute value function, denoted as |x|, is a mathematical function that returns the non-negative value of a number. It measures the distance between a number and zero on the number line.

The absolute value function takes any real number as input and returns its positive value. For positive numbers, the absolute value of a is a itself, while for negative numbers, it returns the negative of a. Mathematically, this can be defined as:

|a| =

– a, if a < 0
- a, if a ≥ 0
The absolute value function is always non-negative or zero. For example, |3| = 3 and |-5| = 5. The absolute value operation removes the sign of a number, making it positive.
Graphically, the absolute value function is represented by a V-shaped graph, known as a "V-curve" or "abs(x) graph". The vertex of the V-curve is at the origin (0, 0), and the arms of the V extend upwards and downwards, parallel to the y-axis. The graph reflects the behavior of the function for both positive and negative values.
The absolute value function is widely used in various mathematical applications, such as solving absolute value equations and inequalities, finding distances between points, calculating magnitudes, and defining piecewise functions. It is an essential concept in algebra, geometry, calculus, and other areas of mathematics.

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