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

Absolute Value Function

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

The absolute value function, denoted as |x|, is a mathematical function that returns the non-negative value of a real number. In other words, it gives the distance of a number from zero on the number line. The absolute value of a number is always positive or zero.

The absolute value function can be defined as follows:
– For any positive number x, |x| = x.
– For any negative number x, |x| = -x.
– For zero, |0| = 0.

For example, if we take the number -5, its absolute value is |-5| = 5 because 5 units away from zero in the positive direction on the number line. Similarly, the absolute value of 5 is |5| = 5, as it is already a positive number. Hence, both -5 and 5 have the same absolute value of 5.

The absolute value function has various applications in mathematics, particularly in solving equations and inequalities. It helps us understand the magnitude or size of a number, disregarding its sign.

Graphically, the absolute value function produces a V-shaped graph. It is symmetric about the y-axis, meaning that the distance from any point on the graph to the y-axis is equal to the distance from its reflection across the y-axis.

More Answers: