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# Write properties absolute value. # Write properties absolute value.

Question
Piecewise-Defined Functions asked 2021-03-08
Write properties absolute value.

## Answers (1) 2021-03-09
Step 1
According to the question, we have to write the properties of absolute value.
In mathematics, absolute value or modulus is same thing and it is defined as the non-negative value of y without regard to its sign. Namely, $$\displaystyle{\left|{{y}}\right|}={y}$$ if y is positive, and $$\displaystyle{\left|{{y}}\right|}=−{y}$$ if y is negative.
Absolute values are often used in problems involving distance and are sometimes used with inequalities.
Step 2
As per the discussion, the absolute value can be defined as the distance of a number on the number line from 0 without considering which direction from zero the number lies.
The properties of the absolute values are as follows,
1- The absolute value of a number is never negative.
2- The absolute value of a number means the distance from 0. -7 is 7 units away from 0.
3- Its often used in problems involving distance and are sometimes used with inequalities.
For example, the absolute value of 4 is 4, and the absolute value of −4 is also .
Hence, basically the distance of a number on the number line from 0 without considering which direction from zero the number lies.

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