Quick questions on Graphing rational functions explained: H2 Mathematics Functions and Graphs

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is quadratic over linear?

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For

\dfrac{ax^2 + bx + c}{dx + e}

, polynomial division gives a linear term plus a remainder fraction, so the curve has an oblique (slant) asymptote. These curves usually have a maximum and a minimum found by differentiation, and the two stationary values are separated by the vertical asymptote.

What is q1?

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Find the asymptotes of

y = \dfrac{3x - 1}{x + 2}

. [2 marks]

What is q2?

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The curve

y = \dfrac{x^2 + 4}{x}

has stationary points. Find them and their nature. [3 marks]

What is q3?

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Explain how to find an oblique asymptote of a rational function. [2 marks]

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