| Date | November 2014 | Marks available | 2 | Reference code | 14N.1.hl.TZ0.1 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The function \(f\) is defined by \(f(x) = \frac{1}{x},{\text{ }}x \ne 0\).
The graph of the function \(y = g(x)\) is obtained by applying the following transformations to
the graph of \(y = f(x)\) :
\({\text{a translation by the vector }}\left( {\begin{array}{*{20}{c}}{ - 3} \\ 0 \end{array}} \right);\) \({\text{a translation by the vector }}\left( {\begin{array}{*{20}{c}} 0 \\ 1 \end{array}} \right);\)
Find an expression for \(g(x)\).
State the equations of the asymptotes of the graph of \(g\).
Markscheme
\(g(x) = \frac{1}{{x + 3}} + 1\) A1A1
Note: Award A1 for \(x + 3\) in the denominator and A1 for the “\( + 1\)”.
[2 marks]
\(x = - 3\) A1
\(y = 1\) A1
[2 marks]
Total [4 marks]
Examiners report
This question was generally well done. A few candidates made a sign error for the horizontal translation. A few candidates expressed the required equations for the asymptotes as ‘inequalities’, which received no marks.
This question was generally well done. A few candidates made a sign error for the horizontal translation. A few candidates expressed the required equations for the asymptotes as ‘inequalities’, which received no marks.
