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Absolute Value Function
The absolute value function is defined by a rule which is divided into two cases. DEFINITION The absolute value function   is defined by The absolute value of x gives the distance between x and 0. It is always positive or zero. For example, 3 = 3, 3 = 3, 0=0. The domain of the absolute value function is the whole real line R while its range is the interval [0, ∞). The absolute value function can also be described by the rule Its graph is given by the equation y = . The graph is the V shown in Figure 1.2.10. Figure 1.2.10 If a and b are two points on the real line, then from the definition of x we see that Thus a — b is the difference between the larger and the smaller of the two numbers. In other words, a  b is the distance between the points a and b, as illustrated in Figure 1.2.11. Figure 1.2.11 For example, 2  5 = 3, 4  ( 4) = 8. Here are some useful facts about absolute values.


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