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Draw the graph of the signum function f(...

Draw the graph of the signum function `f(x)={{:(|x|/x, " when ", x ne0),(0," when ", x=0):}`

Text Solution

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Clearly, (0,0), is a point on the graph. Now, when |x|= -x and therefore,
f(x) = -1 for all value of x lt 0.
Hence, the graph may be drawn, as shown in the adjoining figure.
Clearly, the funcation is broken (i.e, it is discontinuous ) at each of the points x=-1 and 1.
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