 # Exam-Style Questions on Graph

## Problems on Graph adapted from questions set in previous exams.

### 1.

GCSE Higher

The diagram shows part of the graph $$y=x^2-3x+6$$. (a) By drawing a suitable straight line, use your graph to find estimates for the solutions of $$x^2 - 4x + 2 = 0$$ to one decimal place.

(b) A is the point (2,4). Calculate an estimate for the gradient of the graph at the point A.

### 2.

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).

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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