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Class 11MathematicsRelations and FunctionsGraphs of standard functionsExpert
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At which value of \(x\) will the graph of \(f(x)=\operatorname{sgn}(x-2)\) have a jump discontinuity?

Answer and explanation

Correct answer: \(x=2\)

The function \(\operatorname{sgn}(x-2)\) equals \(-1\) when \(x-2<0\) and \(1\) when \(x-2>0\). Its value changes when \(x-2=0\), giving \(x=2\); the unequal one-sided limits therefore produce a jump discontinuity there. \(x=0\) would be the change point for \(\operatorname{sgn}(x)\), not for this shifted function. Exam tip: for \(\operatorname{sgn}(g(x))\), first solve \(g(x)=0\) to locate possible jumps.

Related tags

GraphsSignum FunctionJump DiscontinuityGraphs Of Standard FunctionsRelations And FunctionsMathematicsClass 11 Mcq
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