IB Maths AA HL Ahl 2 13 Hl Further Rational Functions Questions

Practise analysing rational functions through factors, asymptotes, intercepts, range and stationary points, then solving inequalities with domain restrictions.

Exam points

Factor or inspect the numerator and denominator to find excluded x-values, intercepts and vertical asymptotes of a rational function.
Use polynomial division or end behaviour to derive horizontal or oblique asymptotes and sketch the corresponding branches.
Use asymptotes, intercepts, range and stationary-point conditions to determine unknown parameters or classify the graph.
Solve or interpret a rational-function inequality or model by tracking sign changes, domain restrictions and the graphâ€™s asymptotic behaviour.

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Study AHL 2.13 (HL)—Further rational functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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The following question explores features of a family of curves. The family is then linked to a homogeneous differential equation.
Consider the curve given by $y=\frac{x\left(x^{2}-16\right)}{x^{2}+16}$ .

Hence, determine the equation of the oblique asymptote to the curve.

hence oblique asymptote is y=x (since $\frac{2 A x}{x^{2}+A} \rightarrow 0$ as $x \rightarrow \pm \infty$ )

Note: Award AO if not given as an equation.

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IB Maths AA HL Ahl 2 13 Hl Further Rational Functions Questions question 1