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Date	May 2019	Marks available	5	Reference code	19M.1.AHL.TZ2.H_5
Level	Additional Higher Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 2
Command term	Sketch	Question number	H_5	Adapted from	N/A

Question

Sketch the graph of $y = \frac{{x - 4}}{{2x - 5}}$ , stating the equations of any asymptotes and the coordinates of any points of intersection with the axes.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

correct shape: two branches in correct quadrants with asymptotic behaviour A1

crosses at (4, 0) and $\left( {0{\text{,}}\,\,\frac{4}{5}} \right)$ A1A1

asymptotes at $x = \frac{5}{2}$ and $y = \frac{1}{2}$ A1A1

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » SL 2.8—Reciprocal and simple rational functions, equations of asymptotes

Show 26 related questions

18N.2.AHL.TZ0.H_8a:
On the following axes, sketch the two possible graphs of $y = f\left( x \right)$ giving the equations of any asymptotes in terms of $p$ and $q$ .
22M.1.SL.TZ2.4a.ii:
Write down the equation of the horizontal asymptote.
22M.1.SL.TZ2.4a.i:
Write down the equation of the vertical asymptote.
22M.1.SL.TZ2.4b:
On the set of axes below, sketch the graph of $y = f (x)$ .

On your sketch, clearly indicate the asymptotes and the position of any points of intersection with the axes.
22M.1.AHL.TZ2.3a.i:
Write down the equation of the vertical asymptote.
21N.1.SL.TZ0.3c:
Sketch the graph of $f$ on the axes below.
21N.1.AHL.TZ0.2a.i:
the vertical asymptote of the graph of $f$ .
21N.1.AHL.TZ0.2a.ii:
the horizontal asymptote of the graph of $f$ .
21N.1.AHL.TZ0.2c:
Sketch the graph of $f$ on the axes below.
21N.1.SL.TZ0.3a.i:
the vertical asymptote of the graph of $f$ .
21N.1.SL.TZ0.3a.ii:
the horizontal asymptote of the graph of $f$ .
21N.1.SL.TZ0.3b.i:
the $x$ -axis.
21N.1.AHL.TZ0.2b.ii:
the $y$ -axis.
18N.2.SL.TZ0.S_3a.i:
For the graph of $f$ , find the $y$ -intercept.
22M.1.SL.TZ2.4c:
Hence, solve the inequality $0 < \frac{2 x - 1}{x + 1} < 2$ .
22M.1.AHL.TZ2.3a.ii:
Write down the equation of the horizontal asymptote.
22M.1.AHL.TZ2.3c:
Hence, solve the inequality $0 < \frac{2 x - 1}{x + 1} < 2$ .
22M.2.SL.TZ1.8a.ii:
find the equation of the horizontal asymptote.
18N.2.SL.TZ0.S_3b:
Hence or otherwise, write down $\mathop {{\text{lim}}}\limits_{x \to \infty } \left( {\frac{{6x - 1}}{{2x + 3}}} \right)$ .
18M.2.SL.TZ2.S_7b:
Write down the equation of the horizontal asymptote to the graph of f.
18M.1.AHL.TZ2.H_10b.i:
Express $g\left( x \right)$ in the form $A + \frac{B}{{x - 2}}$ where A, B are constants.
21N.1.AHL.TZ0.2d:
The function $g$ is defined by $g (x) = \frac{a x + 4}{3 - x}$ , where $x \in ℝ, x \neq 3$ and $a \in ℝ$ .

Given that $g (x) = g^{- 1} (x)$ , determine the value of $a$ .
22M.2.SL.TZ1.8a.i:
write down the equation of the vertical asymptote.
21N.1.SL.TZ0.3b.ii:
the $y$ -axis.
21N.1.AHL.TZ0.2b.i:
the $x$ -axis.
18N.2.AHL.TZ0.H_8b:
Given that $p = \frac{4}{3}$ , $q = \frac{4}{9}$ and A has coordinates $\left( { - \frac{1}{2},\,\,0} \right)$ , determine the possible sets of values for $a$ , $b$ and $c$ .

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Topic 2—Functions

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