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Which of the following standard functions has two separate branches in the first and third quadrants, with both coordinate axes as its asymptotes?

Answer and explanation

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

For \(y=1/x\), x and y have the same sign, so its branches lie in quadrants I and III. Neither x nor y can be zero, making both axes asymptotes. In contrast, \(1/x^2\) remains above the x-axis. Exam tip: use signs and powers to locate branches.

Related tags

Standard FunctionsReciprocal FunctionGraph IdentificationAsymptotesQuadrantsRelations And FunctionsGraphs Of Standard FunctionsMathematics

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