Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for rewriting expressions that involve it.
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Square Root
The square root of a number x, denoted as √x, is a value that, when multiplied by itself, gives x. Square roots can yield both positive and negative results, but the principal square root is the non-negative one. For instance, √4 = 2, but -2 is also a square root of 4, though it is not the principal square root.
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Piecewise Functions
Piecewise functions are defined by different expressions based on the input value. For absolute values, the expression can be rewritten as a piecewise function: |x| = x if x ≥ 0 and |x| = -x if x < 0. This concept is essential for rewriting expressions involving absolute values, as it allows for the correct interpretation of the expression based on the value of the variable.
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