A. Absolute Value
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A. Absolute Value
In the previous Investigation, you may have noticed that sometimes the size of a value is important, but whether it is positive or negative is not. The size of a transaction tells us how much money was transferred, but it does not tell whether a person gained or lost money. When the size of a number, but not the sign, is desired, absolute value can be used.
The absolute value operation does not change zero or positive numbers, but changes negative numbers to positive numbers. As such, the absolute value of a number or expression can also be defined as a piecewise function. In a piecewise function, a different rule is used to define the function for different intervals of the domain.
\(\left| x \right| = \left\{ \begin{align}
&x \thinspace {\rm {for}} \thinspace x \ge 0 \\
-&x \thinspace {\rm{for}} \thinspace x < 0 \end{align}\right. \)
Determining the absolute value of a number is very straightforward. The absolute value of a positive number is the same value. The absolute value of a negative number is its positive equivalent.
The absolute value operation does not change zero or positive numbers, but changes negative numbers to positive numbers. As such, the absolute value of a number or expression can also be defined as a piecewise function. In a piecewise function, a different rule is used to define the function for different intervals of the domain.
\(\left| x \right| = \left\{ \begin{align}
&x \thinspace {\rm {for}} \thinspace x \ge 0 \\
-&x \thinspace {\rm{for}} \thinspace x < 0 \end{align}\right. \)
Determining the absolute value of a number is very straightforward. The absolute value of a positive number is the same value. The absolute value of a negative number is its positive equivalent.