## Exam-Style Questions on Function graphing## Problems on Function graphing adapted from questions set in previous exams. |

## 1. | IB Standard |

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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