91Ó°ÊÓ

Modulus Function Formula

The value of the modulus function is always non-negative. If f(x) is a modulus function, then we have:

This means if the value of x is greater than or equal to 0, then the modulus function takes the actual value, but if x is less than 0 then the function takes minus of the actual value 'x'.

Absolute Value

Absolute value signs make the final result of the operations between them positive. When deciding on the order of operations, treat absolute value bars like parentheses.

|– 3| = 3: The absolute value bars make negative 3 positive.

| 3 | = 3: The absolute value bars leave positive 3 unchanged

– |– 3| = – 3: The absolute value bars make negative 3 positive. Then the negative sign takes effect, and the answer is a negative 3.

– | 3 | = – 3: The absolute value bars leave positive 3 unchanged. Then the negative sign takes effect, and the answer is a negative 3.

We know that: |– 3| = 3: The absolute value bars make negative 3 positive.

According to the property, we can write – 12 < |12| – 12 < 12

The absolute value bars leave positive 12 unchanged and positive.