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Class 11MathematicsRelations and FunctionsGraphs of standard functionsExpert
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What is the horizontal asymptote of the graph of the function \(y=\frac{x+4}{x-2}\)?

Answer and explanation

Correct answer: \(y=1\)

The numerator and denominator are both of degree 1. Therefore, the horizontal asymptote is determined by the ratio of the leading coefficients: \(y=\frac{1}{1}=1\). Hence, \(y=1\) is correct. The line \(x=2\) is the vertical asymptote because the denominator becomes zero there. Exam tip: For a rational function with equal numerator and denominator degrees, divide the leading coefficient of the numerator by that of the denominator to find the horizontal asymptote.

Related tags

Graphs Of FunctionsRational FunctionsHorizontal AsymptoteRelations And FunctionsGraphs Of Standard FunctionsMathematicsClass 11 Mcq
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  2. 2Which relation represents the graph of the rule \(y=x+2\) for the inputs in the set \(A=\{1,3\}\)?
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  7. 7Which shape represents the graph of (f(x)=x^2)?
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