| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.hl.TZ0.3 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
A rational function is defined by \(f(x) = a + \frac{b}{{x - c}}\) where the parameters \(a,{\text{ }}b,{\text{ }}c \in \mathbb{Z}\) and \(x \in \mathbb{R}\backslash \{ c\} \). The following diagram represents the graph of \(y = f(x)\).
Using the information on the graph,
state the value of \(a\) and the value of \(c\);
[2]
a.
find the value of \(b\).
[2]
b.
Markscheme
\(a = 1\) A1
\(c = 3\) A1
[2 marks]
a.
use the coordinates of \((1,{\text{ }}0)\) on the graph M1
\(f(1) = 0 \Rightarrow 1 + \frac{b}{{1 - 3}} = 0 \Rightarrow b = 2\) A1
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
