Overview: What Is Absolute Value?
The absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of 3 is 3, and the absolute value of -3 is also 3. A positive number and its negative have the same absolute value. It is symbolized as |x|, and |-x| has the same value. It can be positive or zero, but never negative.
Properties of Absolute Value
Absolute value can be positive or zero, but never negative. If |a| equals zero, then a must equal zero, because there is no such number as “negative zero”. For any number |ab|= |a| |b|. A number |x| and its negative |-x| will have the same absolute value.
Absolute Value and Distance
The definition of absolute value is closely related to the ideas of distance and magnitude. Whether numbers are plotted along a number line or complex numbers are plotted in a plane, their location in space is their distance from zero. Therefore, the absolute value of the difference between two numbers is the distance between them.
Graphing Absolute Value
Since the absolute value of negative numbers is the same as the absolute value of positive numbers, a line graph will show a convex, symmetrical line on either side of x=0. In fact the only value that is the same point on both sides of the graph is when x=0. it is also a continuous function.
Real World Examples of Absolute Value
Applications of absolute value include measurement of distances, and therefore navigation, transport, and architecture. Sports problems that involve distance (such as measurement between first downs in football) also involve absolute value. In addition, because the normal curve in statistics refers to the distance from the mean, statistical analysis can also use absolute value.
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