IB Maths AI HL 2.3 Graphing functions and asymptotic behaviour Question Bank

Practise IB Maths AI HL 2.3 by analysing function sketches, limiting behaviour and trajectories in applied models.

Exam points

Sketch a function using limits, turning points, intercepts and the stated domain.
Use limiting behaviour and derivative information to justify the shape of a model graph.
Interpret a multi-variable or trajectory graph and connect its features to the model parameters.

[Maximum number: 3]

A student investigating the relationship between chemical reactions and temperature finds the Arrhenius equation on the internet.

k=A \mathrm{e}^{-\frac{c}{T}}

This equation links a variable k with the temperature T, where A and c are positive constants and T>0.

Given that $\lim_{T\to\infty}k=A$ and $\lim_{T\to0}k=0$ , sketch the graph of k against T.

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