Understanding the Absolute Value Function | Definition, Graph, and Applications

Absolute Value Function

The absolute value function, often denoted as |x|, is a mathematical function that gives the distance of a number from zero on the number line

The absolute value function, often denoted as |x|, is a mathematical function that gives the distance of a number from zero on the number line. It measures the magnitude or size of a real number without considering its sign.

Mathematically, the absolute value function can be defined as follows:

For any real number x, if x is positive or zero, |x| = x.
If x is negative, |x| = -x.

So basically, the absolute value of a number conceptually removes the negative sign if the number is negative and keeps the number as is if it is positive or zero.

For example:
– |3| = 3, since 3 is positive.
– |-5| = 5, as the absolute value removes the negative sign from -5.
– |0| = 0, since 0 has no negative or positive direction.

Graphically, the absolute value function creates a V-shaped graph, also known as a “V-curve” or “piecewise function.” The vertex of the V-curve is at the point (0, 0), and the line of symmetry is the y-axis. As the function can only result in non-negative values, any value of x will output its positive equivalent.

The absolute value function has various uses in mathematics, including solving equations, inequalities, and finding distances and differences between numbers. Its properties and applications are explored in algebra, calculus, and other mathematical branches.

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