## Question 7:

### Part (i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Asymptotes: $y=3$, $x=2$, $x=-1$ | B1 | |
| Crosses axes at $(0,3)$ | B1 | (both) Allow $x=2$, $x=-1$. Must see values for x and y if not written as co-ordinates |
| $\left(-\dfrac{2}{3}, 0\right)$, $(3, 0)$ | B1, B1 | (both) Must see values for x and y if not written as co-ordinates |
| | **[4]** | |

### Part (ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Graph with intercepts labelled | B1 | Intercepts labelled (single figures on axes suffice) |
| Asymptotes correct and labelled | B1 | Allow $y=3$ shown by intercept labelled at $(0,3)$ and $x=2$ and $x=-1$ likewise |
| Three correct branches | B2 | Three correct branches (-1 each error). Any poorly illustrated asymptotic approaches penalised once only |
| When x is large and positive, graph approaches $y=3$ from below, e.g. for $x=100$, $\frac{302\times97}{98\times101} = 2.9\ldots$ | B1 | Approaches to $y=3$ justified. There must be a result for y |
| When x is large and negative, graph approaches $y=3$ from above, e.g. for $x=-100$, $\frac{-298\times-103}{-102\times-99} = 3.03\ldots$ | | |
| | **[5]** | |

### Part (iii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $y \geq 3 \Rightarrow 0 \leq x < 2$ or $x < -1$ | B1 | $x < -1$ |
| | B1B1 | $0 \leq x < 2$ (B1 for $0 < x < 2$ or $0 \leq x \leq 2$) isw any more shown |
| | **[3]** | |

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