Strategy 2: Interpret the Corresponding Function

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Strategy 2: Interpret the Corresponding Function

In the Investigation, you may have noticed that the graph of an absolute value function, \(y = \left| {f\left( x \right)} \right|\), is related to the corresponding function \(y = f\left( x \right)\). Any portion of the graph of \(y = f\left( x \right)\) that lies below the \(x\)-axis is reflected above the \(x\)-axis to produce the graph of \(y = \left| {f\left( x \right)} \right|\). This relationship can be written using piecewise notation as:

\(\left|{f\left(x\right)}\right| = \left\{\begin{align}
&f\left(x\right){\rm\thinspace {for}}\thinspace f\left( x \right) \ge 0 \\
-&f\left(x\right){\rm\thinspace {for}}\thinspace f\left( x \right) < 0  \end{align} \right.\)