# Exam-Style Question on Graphing Functions

## A mathematics exam-style question with a worked solution that can be revealed gradually

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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 $$y=\frac{2}{x^2}-x, x\neq 0$$.

 $$x$$ $$y$$ -3 -2 -1 -0.5 0.5 1 2 3 4 3.2 2.5 8.5 7.5 1 -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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