2021 SJI P1 Q3

2021 SJI P1 Q3

IB Year 5 | Grade 11
9 marks

Consider the function \(\mathrm{f}(x)=2(x-1)^2-2\).

  1. State the minimum value of \(\mathrm{f}\).[1]
  2. Find the zeros of \(y=\mathrm{f}(x)\).[2]
  3. State the coordinates of the turning point of \(y=\dfrac1{\mathrm{f}(x)}\).[2]
  4. Sketch the graph of \(y=\dfrac1{\mathrm{f}(|x|)}\) in the given axes on the next page, clearly indicating the asymptotes and turning points.[4]

Solution:

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Answer:(a) \(-2\) (b) \(0,2\) (c) \(\left(1,-\dfrac12\right)\) (d) Asymptotes \(x=-2,0,2\) and \(y=0\); maxima \(\left(\pm1,-\dfrac12\right)\).

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