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2020 IGCSE Additional Mathematics February/March 0606/22 Q8

2020 IGCSE Additional Mathematics February/March 0606/22 Q8

6 marks

The diagram shows the graph of \(\mathrm{f}(x)=a\cos bx+c\) for \(0\le x\le\dfrac{8\pi}{3}\) radians.

  1. Explain why \(\mathrm{f}\) is a function.[1]
  2. Write down the range of \(\mathrm{f}\).[1]
  3. Find the value of each of the constants \(a\), \(b\) and \(c\).[4]

Solution:

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Answer:(a) Each value of \(x\) in the domain is mapped to exactly one value of \(\mathrm{f}(x)\) (b) \(-5\le\mathrm{f}(x)\le1\) (c) \(a=3\), \(b=\dfrac34\), \(c=-2\)

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