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Class 11MathematicsRelations and FunctionsGraphs of standard functionsEasy
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How many times does the graph of (f(x)=x^2+4) cut the (x)-axis?

Answer and explanation

Correct answer: (0) times

The direct answer is A: the graph cuts the x-axis 0 times. A point on the x-axis has y=0. For this graph, y=x^2+4. Since \\(x^2\ge0\\) for every real x, we have \\(x^2+4\ge4\\). Thus y can never be 0, so there is no x-intercept. A is correct. Option B would require one real solution of \\(x^2+4=0\\), but this gives \\(x^2=-4\\), impossible for real x. Option C would mean two x-intercepts; although a usual upward quadratic may have two, this one is shifted four units above the x-axis and has none. Option D has no algebraic or graphical basis. The vertex is \\( (0,4)\\), and the entire parabola lies above the x-axis. Memory cue: to count x-axis crossings, set y=0 and count real solutions.

Related tags

Relations-FunctionsStandard-GraphsNo-X-Intercept
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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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