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Class 11MathematicsRelations and FunctionsGraphs of standard functionsEasy
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What is the maximum value of the function \(f(x)=-|x|+6\)?

Answer and explanation

Correct answer: 6

For every real \(x\), \(|x|\ge 0\), so \(-|x|\le 0\) and hence \(f(x)=-|x|+6\le 6\). At \(x=0\), \(f(0)=6\), so the maximum value is 6. The value 0 occurs at \(x=\pm6\), but it is not the maximum. Exam tip: the graph of \(-|x|\) opens downward, with its vertex at \(x=0\).

Related tags

Standard-FunctionsModulus-FunctionMaximum-ValueGraphs Of Standard FunctionsRelations And FunctionsMathematicsClass 11 Mcq
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10 more MCQs
  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?
  4. 4If \(f:\{1,2,3,4\}\to\{1,2,3,4\}\) and \(f(x)=5-x\), which of the following is the graph of \(f\)?
  5. 5What is the usual graph of the function (f(x)=x)?
  6. 6What is the graph of (f(x)=c), where (c) is a constant?
  7. 7Which shape represents the graph of (f(x)=x^2)?
  8. 8In which direction does the graph of (f(x)=-x^2) open?
  9. 9The graph of (f(x)=|x|) is symmetric about which axis?
  10. 10Through which point does the graph of f(x)=x³ pass?
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