# Exam-Style Questions on Function graphing

## Problems on Function graphing adapted from questions set in previous Mathematics 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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