Modulus Function
= max {x, â€“x}
Domain: R; Range: [0, âˆž) 

Properties of modulus function
 x = a â‡’ Points on the real number line whose distance from origin is a
 x â‰¤ a â‡’ x^{2} â‰¤ a^{2} â‡’ Points on the real number line whose distance from origin is a or less than a
 x â‰¥ a â‡’ x^{2} â‰¥ a^{2} â‡’ Points on the real number line whose distance from origin is a or greater than a. â‡’ x â‰¤ â€“a or x â‰¥ a; (a â‰¥ 0)
 a â‰¤ x â‰¤ b â‡’ a^{2} â‰¤ x^{2} â‰¤ b^{2} â‡’ x âˆˆ [â€“b, â€“a] âˆª [a, b]
 x + y = x + y â‡” x and y have same sign or at least one of x and y is zero or xy â‰¥ 0
 x Â± y â‰¤ x+ y
 x Â± y â‰¥ x â€“ y