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Class 11MathematicsRelations and FunctionsGraphs of standard functionsEasy
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Which point is not on the graph of (f(x)=\sqrt{x})?

Answer and explanation

Correct answer: ((-1,1))

The direct answer is D: \\((-1,1)\\) is not on the graph. For \\(y=\sqrt{x}\\), the input x must be non-negative, and the point must satisfy y equal to the principal square root of x. Check A: \\(\sqrt9=3\\), so \\( (9,3)\\) is on the graph. Check B: \\(\sqrt{16}=4\\), so \\( (16,4)\\) is on it. Check C: \\(\sqrt1=1\\), so \\( (1,1)\\) is on it. Check D: x=-1 is outside the real domain of the square-root function; \\(\sqrt{-1}\\) is not a real number, so \\((-1,1)\\) cannot lie on this real graph. D is correct. A, B and C each satisfy the equation exactly. Do not confuse \\(y=\sqrt{x}\\) with \\(y^2=x\\), which would also include negative y-values; the square-root function uses the non-negative principal value.

Related tags

Standard-FunctionsSquare-Root-FunctionPoint-Check
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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?
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  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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