Draw the graph of sgn [x], sgn is the signum function

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Solution

The correct option is D

We know sgn $(x) = 1 i f x > 0$

$= 0 i f x = 0$

$= - 1 i f x < 0$

$\Rightarrow$ sgn [x] $= 1 i f [x] > 0$

$= 0 i f [x] = 0$

$= - 1 i f [x] < 0$

$[x] > 0 \Rightarrow x \geq 1$

$[x] = 0 \Rightarrow x ϵ [0, 1)$

$[x] < 0 \Rightarrow x < 0$

So sgn[x] $= 1 i f x > 1$ or x = 1

$= 0 i f x ϵ [0, 1)$

$= - 1 i f x < 0$

So the graph will be

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