Understanding the Absolute Value Function: Definition, Graph, and Properties

absolute value function

f(x) = |x|

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

For example, let’s consider the absolute value of -5. In this case, the function |x| would evaluate to |(-5)| = 5, because -5 is 5 units away from the origin on the number line.

Similarly, if we take the absolute value of 3, the function |x| would evaluate to |3| = 3, as 3 is also 3 units away from the origin.

In general, the absolute value function is defined as follows:

|x| = x, if x ≥ 0
-x, if x < 0 This definition highlights that if a number is positive or zero, its absolute value is the number itself. However, if a number is negative, its absolute value is the negation of the number (i.e., the number without its negative sign). Graphically, the absolute value function is represented by a V-shaped graph, known as a "V-curve" or "V-tick." It is symmetric about the y-axis, with its vertex at the origin. The function is always positive or zero, as it represents distances, which are non-negative.

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