| Date | May 2011 | Marks available | 6 | Reference code | 11M.1.hl.TZ1.10 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Sketch, Write down, and Indicate | Question number | 10 | Adapted from | N/A |
Question
The diagram below shows the graph of the function \(y = f(x)\) , defined for all \(x \in \mathbb{R}\),
where \(b > a > 0\) .
Consider the function \(g(x) = \frac{1}{{f(x - a) - b}}\).
Find the largest possible domain of the function \(g\) .
On the axes below, sketch the graph of \(y = g(x)\) . On the graph, indicate any asymptotes and local maxima or minima, and write down their equations and coordinates.
Markscheme
\(f(x - a) \ne b\) (M1)
\(x \ne 0\) and \(x \ne 2a\) (or equivalent) A1
[2 marks]
vertical asymptotes \(x = 0\), \(x = 2a\) A1
horizontal asymptote \(y = 0\) A1
Note: Equations must be seen to award these marks.
maximum \(\left( {a, - \frac{1}{b}} \right)\) A1A1
Note: Award A1 for correct x-coordinate and A1 for correct y-coordinate.
one branch correct shape A1
other 2 branches correct shape A1
[6 marks]
Examiners report
A significant number of candidates did not answer this question. Among the candidates who attempted it there were many who had difficulties in connecting vertical asymptotes and the domain of the function and dealing with transformations of graphs. In a few cases candidates managed to answer (a) but provided an answer to (b) which was inconsistent with the domain found.
A significant number of candidates did not answer this question. Among the candidates who attempted it there were many who had difficulties in connecting vertical asymptotes and the domain of the function and dealing with transformations of graphs. In a few cases candidates managed to answer (a) but provided an answer to (b) which was inconsistent with the domain found.
