IB Maths AA HL 2.13 Further rational functions Question Bank

Practise IB Mathematics HL 2.13 by applying further rational functions methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 1]

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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AHL 2.13 (HL)—Further rational functions question 1