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Exam-Style Question on Graphing FunctionsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 114. This question is similar to one that appeared on a IGCSE Extended paper in 2014. The use of a calculator is allowed.
The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).
| \(x\) | -3 | -2 | -1 | -0.5 | 0.5 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| \(y\) | 3.2 | 2.5 | 8.5 | 7.5 | 1.0 | -2.8 |
(a) Complete the table of values.
(b) Draw the graph of \(y=\frac{2}{x^2}-x\) for \(-3\le x \le -0.5\) and \(0.5\le x\le 4\).
(c) Use your graph to solve the equation \(\frac{2}{x^2}-x-3=0\)
(d) Use your graph to solve the equation \(\frac{2}{x^2}-x=1-2x\)
(e) By drawing a suitable tangent, find an estimate of the gradient of the curve at the point where x = 1.
(f) Using algebra, show that you can use the graph at \(y=0\) to find \(\sqrt[3]2\)
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