Sports problems that involve distance (such as measurement between first downs in football) also involve absolute value. it is also a continuous function.Īpplications of absolute value include measurement of distances, and therefore navigation, transport, and architecture. In fact the only value that is the same point on both sides of the graph is when x=0.
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. Therefore, the absolute value of the difference between two numbers is the distance between them. 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. The definition of absolute value is closely related to the ideas of distance and magnitude. A number |x| and its negative |-x| will have the same absolute value. If |a| equals zero, then a must equal zero, because there is no such number as “negative zero”. It can be positive or zero, but never negative.Ībsolute value can be positive or zero, but never negative. It is symbolized as |x|, and |-x| has the same value. A positive number and its negative have the same absolute value. Therefore, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number is its distance from zero on the number line.
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