the absolute value function
The absolute value function, denoted as |x|, is a mathematical function that returns the positive value of a number, regardless of its sign
The absolute value function, denoted as |x|, is a mathematical function that returns the positive value of a number, regardless of its sign. It measures the distance or magnitude of a number from zero on a number line.
The absolute value function has a simple pattern: if the input number is positive or zero, the output is the same as the input. However, if the input number is negative, the output is the opposite sign of the input number.
Mathematically, the absolute value function can be defined as follows:
| x | = x if x ≥ 0
| x | = -x if x < 0
Here are a few examples to illustrate how the absolute value function works:
1. |5| = 5
The input number is positive, so the absolute value function returns the same number.
2. |-7| = 7
The input number is negative, so the absolute value function returns the positive value of the number.
3. |0| = 0
The input number is zero, so the absolute value function returns the same number.
4. |-2.5| = 2.5
Similar to example 2, the input number is negative, so the absolute value function returns the positive value of the number.
The absolute value function can be used in various mathematical expressions and equations. For instance, it is commonly used to simplify algebraic expressions, solve absolute value equations, and represent inequalities.
In summary, the absolute value function is a mathematical tool used to find the positive value of any real number, irrespective of its sign. It has a simple pattern, where the function returns the input number if it is positive or zero, or returns the opposite sign if the input number is negative.
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