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Question id: 59. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is allowed.

Let \(f(x)=\frac{3x}{x-q}\), where \(x \neq q\).

(a) Write down the equations of the vertical and horizontal asymptotes of the graph of \(f\).

The vertical and horizontal asymptotes to the graph of \(f\) intersect at the point Q(1, 3).

(b) Find the value of q.

(c) The point P(x, y) lies on the graph of \(f\). Show that PQ = \(\sqrt{(x-1)^2+(\frac{3}{x-1})^2}\)

(d) Hence find the coordinates of the points on the graph of \(f\) that are closest to (1, 3).

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