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

Analyse further rational functions, including asymptotes, discontinuities and end behaviour.
Solve rational-function equations or determine parameters using complete evidence.

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