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Which description best matches the graph of \(f(x)=|x|\)?

Answer and explanation

Correct answer: A V-shaped graph with vertex at \((0,0)\) and symmetry about the y-axis

For \(f(x)=|x|\), the value is \(|x|\ge 0\). When \(x\ge0\), \(|x|=x\) (a line with slope \(1\)); when \(x<0\), \(|x|=-x\) (a line with slope \(-1\)). These two rays meet at \(x=0\), giving a V-shape with vertex at \((0,0)\). The function depends only on \(x\) through \(|x|\), so it is symmetric about the y-axis.

Related tags

Absolute ValueGraphs Of Standard FunctionsShape Of GraphCoordinate Geometry

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