Absolute Value

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Definition

Absolute Value
  • Is the value for a real number, disregarding the sign. Written \left|x\right|.
  • Mathematically defined as:
\left|x\right|=x\text {  if  }x\geqq 0

\left|x\right|=-x\text {  if  }x<0
  • Geometrically, \left|x\right| is the distance of x \text { to } 0\,, and from -x \text { to } 0\,.



Examples

Image:Absolute-Value.png
\left|+3\right| = 3

\left|-45\right| = 45

\left|0\right| = 0

\left|+5\right| =\left|-5\right| = 5


Absolute value properties

\text{1) if }\left|x\right| = a\qquad\text{then}\quad x=a \qquad\text{or}\quad x=-a

\text{2) if }\left|x\right| < a\qquad\text{then}\quad -a<x<a

\text{3) if }\left|x\right| > a\qquad\text{then}\quad x>a \qquad\text{or}\quad x<-a

\text{4) }\left|x\right|^2 = x ^ 2

\text{5)  }\left|x\right| = sqr(x^2)




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