| Date | May 2011 | Marks available | 3 | Reference code | 11M.1.hl.TZ2.5 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Sketch | Question number | 5 | Adapted from | N/A |
Question
The diagram shows the graph of y = f(x) . The graph has a horizontal asymptote at y = 2 .
Sketch the graph of \(y = \frac{1}{{f(x)}}\).
[3]
a.
Sketch the graph of \(y = x{\text{ }}f(x)\) .
[3]
b.
Markscheme
A3
Note: Award A1 for each correct branch with position of asymptotes clearly indicated.
If x = 2 is not indicated, only penalise once.
[3 marks]
a.
A3
Note: Award A1 for behaviour at \(x = 0\), A1 for intercept at \(x = 2\) , A1 for behaviour for large \({\left| x \right|}\) .
[3 marks]
b.
Examiners report
Many candidates were able to find the reciprocal but many struggled with the second part. Sketches were quite poor in detail.
a.
Many candidates were able to find the reciprocal but many struggled with the second part. Sketches were quite poor in detail.
b.
Syllabus sections
Topic 2 - Core: Functions and equations » 2.2 » The graph of a function; its equation \(y = f\left( x \right)\) .
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