absolute value function
The absolute value function is a mathematical function that returns the non-negative value (magnitude) of a given number, regardless of its sign
The absolute value function is a mathematical function that returns the non-negative value (magnitude) of a given number, regardless of its sign. It is denoted by the mathematical symbol |x|, where x represents the number.
The absolute value function can be defined as follows:
For any real number x, if x is greater than or equal to 0, then the absolute value of x is x itself.
|x| = x, if x ≥ 0.
If x is less than 0, then the absolute value of x is the negation of x (i.e., the positive value of x).
|x| = -x, if x < 0.
To better understand the concept, let's consider some examples:
Example 1: Find the absolute value of -5.
Here, -5 is less than 0, so we take the negation of -5, which is 5. Therefore, the absolute value of -5 is 5.
Example 2: Find the absolute value of 7.
Here, 7 is greater than or equal to 0, so the absolute value of 7 is 7.
Example 3: Find the absolute value of 0.
Since 0 is neither greater than or equal to 0 nor less than 0, we consider it as a non-negative value. Therefore, the absolute value of 0 is simply 0.
The absolute value function can also be expressed graphically. It produces a V-shaped graph that intersects the x-axis at the origin (0,0). The graph is symmetric about the y-axis.
In summary, the absolute value function returns the non-negative value of a given number. It is defined as the value of the number itself if it is greater than or equal to 0, and the negation of the number if it is less than 0. The absolute value function is represented by the symbol |x| and its graph is a V-shape.
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