Year 12 · Specialist Mathematics

Sketching graphs

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Practise the method.

Asymptotes, intercepts and rational function behaviour.

Example 1

Rational graph with two separate branches, an adjustable viewing window and a probe.xy0Inspect the end behaviour as the viewing window widens
Explore the curve’s behaviour near the break and far from it. Use the equation to identify exact asymptotes.
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Answer:

Example 2

Rational graph with two separate branches, an adjustable viewing window and a probe.xy0Inspect the two sides of the vertical break
Explore the curve’s behaviour near the break and far from it. Use the equation to identify exact asymptotes.
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Answer:

Example 3

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Answer: