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Which of the following standard functions has a graph symmetric about the origin, with both coordinate axes as asymptotes?

Answer and explanation

Correct answer: \(y=\frac{1}{x}\)

For \(y=\frac{1}{x}\), \(f(-x)=-f(x)\), so its graph is symmetric about the origin. The lines \(x=0\) and \(y=0\) are its asymptotes. Exam tip: \(1/x^2\) is symmetric about the y-axis, not the origin.

Related tags

Standard FunctionsReciprocal FunctionGraph SymmetryAsymptotesRelations And FunctionsClass 11 MathematicsGraphs Of Standard FunctionsMathematics

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