Understanding the Absolute Value Function | Definition, Applications, and Graphical Representation

Absolute Value Function

The absolute value function is a mathematical function that gives the distance between a given number and zero on the number line

The absolute value function is a mathematical function that gives the distance between a given number and zero on the number line. It is denoted by the symbol “|” and can be defined as follows:

For any real number x, the absolute value of x is represented as |x| and is defined as:

– |x| = x, if x is greater than or equal to 0.
– |x| = -x, if x is less than 0.

In simpler terms, the absolute value function gives the positive value of a number, regardless of its sign. It essentially “absolutizes” a number, removing its negativity.

For example:
– |3| = 3, because 3 is already positive.
– |-5| = 5, because -5 becomes positive.
– |0| = 0, because the distance between 0 and 0 is 0.

The absolute value function is often used in various mathematical contexts, particularly in solving equations and inequalities. It is also commonly used to calculate distances, such as the distance between two points on a number line or in a coordinate plane.

Graphically, the absolute value function is represented by a V-shaped graph, called a “V-shaped graph, where the vertex is at (0, 0) and the arms extend infinitely in both positive and negative directions. The graph reflects the nature of the function, as it emphasizes that regardless of the value of x, the result is always positive or zero.

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