# Absolute value

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Absolute value is the numerical value irrespective of the sign. If we consider a number line, it is the distance on a number line without considering the direction. Absolute value of -2 is 2.

NOTE:
• An absolute value function is differentiable everywhere except at 0
• In the interval (-∞,0] the absolute value function is monotonically decreasing where as in the interval [0, ∞) it is monotonically increasing.
• It is an even function because a positive and negative number has the same absolute value.

Example:  abs (-4) or | -4| is 4
1) abs(29) is
(a) 29        (b) -29        (c) 0        (d) undefined

2) |6 – 9| and |9 – 6|
(a) 3 and -3         (b) -3 and 3        (c) -3 and -3        (d) 3 and 3

3) |-3 x 7| and - |-12|
(a) 21 and 12        (b) -21 and -12         (c) -12 and 12        (d) 21 and -12

4) abs(0)
(a) Neither negative nor positive        (b) 0          (c) Undefined        (d) Either positive or negative