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Class 11MathematicsRelations and FunctionsGraphs of standard functionsExpert
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Which statement is correct about the graph of \(f(x)=\lfloor x\rfloor\) at \(x=3\)?

Answer and explanation

Correct answer: The graph has a jump discontinuity

For the greatest integer function \(f(x)=\lfloor x\rfloor\), values just to the left of \(x=3\) approach 2, whereas \(f(3)=3\) and values just to the right are 3. Thus the left-hand and right-hand limits are different, so there is a jump discontinuity at \(x=3\). The function is defined for every real \(x\), making option D incorrect. Exam tip: The graph of \(\lfloor x\rfloor\) has a jump discontinuity at every integer.

Related tags

Relations And FunctionsGraphsGreatest Integer FunctionDiscontinuityStandard FunctionsGraphs Of Standard FunctionsMathematicsClass 11 Mcq
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  1. 1If f(x)=x^2 and A={1,2,3} is the domain of f, which of the following is the graph of f on A?
  2. 2Which relation represents the graph of the rule \(y=x+2\) for the inputs in the set \(A=\{1,3\}\)?
  3. 3If f(x)=3x and its domain is A={0,1,2}, which of the following is the graph of the function defined on A?
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  7. 7Which shape represents the graph of (f(x)=x^2)?
  8. 8In which direction does the graph of (f(x)=-x^2) open?
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