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Functions and Graphs

Quick questions on Transformations of graphs 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 are wrong order of vertical operations?
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a f(x)+da\,\mathrm{f}(x) + d stretches first, then translates; reversing them gives a different graph.
What are not moving the asymptotes?
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Asymptotes transform with the curve; a translated curve has translated asymptotes.
What is q1?
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Describe the transformation taking y=f(x)y = \mathrm{f}(x) to y=f(x)−4y = \mathrm{f}(x) - 4. [1 mark]
What is q2?
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The point (1,6)(1, 6) lies on y=f(x)y = \mathrm{f}(x). Find its image on y=f(2x)y = \mathrm{f}(2x). [2 marks]
What is q3?
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Describe fully the transformations mapping y=cos⁡xy = \cos x to y=cos⁡(x−π2)y = \cos(x - \frac{\pi}{2}). [2 marks]

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