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Functions and Graphs

Quick questions on Asymptotes and curve features explained: H2 Mathematics Functions and Graphs

5short 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 behaviour at infinity?
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To find horizontal or oblique behaviour, divide by the highest power of xx in the denominator, or carry out polynomial division. Whatever the remainder fraction tends to zero leaves the dominant part, which is the asymptote. Noting whether the curve approaches from above or below sharpens the sketch.
What is symmetry?
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Spotting symmetry halves the sketching work.
What is q1?
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State the asymptotes of y=5x−2y = \dfrac{5}{x - 2}. [2 marks]
What is q2?
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Determine whether f(x)=x3−x\mathrm{f}(x) = x^3 - x is even, odd or neither. [2 marks]
What is q3?
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Explain how to detect an oblique asymptote and find its equation. [2 marks]

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