21N.1.SL.TZ0.3

pestleMathematicsAASLPaper 121N· sl-2-8-reciprocal-and-simple-rational-functions-equations-of-asymptotessource ↗

The function $f$ is defined by $f (x) = \frac{2 x + 4}{3 - x}$ , where $x \in ℝ, x \neq 3$ .

Write down the equation of

Find the coordinates where the graph of $f$ crosses

the vertical asymptote of the graph of $f$ .

[1]

a.i.

the horizontal asymptote of the graph of $f$ .

[1]

a.ii.

the $x$ -axis.

[1]

b.i.

the $y$ -axis.

[1]

b.ii.

Sketch the graph of $f$ on the axes below.

[1]

Markscheme / solution

$x = 3$ A1

[1 mark]

a.i.

$y = - 2$ A1

[1 mark]

a.ii.

$(- 2, 0)$ (accept $x = - 2$ ) A1

[1 mark]

b.i.

$(0, \frac{4}{3})$ (accept $y = \frac{4}{3}$ and $f (0) = \frac{4}{3}$ ) A1

[1 mark]

b.ii.

Note: Award A1 for completely correct shape: two branches in correct quadrants with asymptotic behaviour.

[1 mark]

Examiners’ report

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a.i.

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a.ii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]