16N.1.AHL.TZ0.H_3

pestleMathematicsAIHLPaper 116N· sl-2-2-functions-notation-domain-range-and-inverse-as-reflectionsource ↗

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 $y = f(x)$ .

N16/5/MATHL/HP1/ENG/TZ0/03

Using the information on the graph,

state the value of $a$ and the value of $c$ ;

[2]

find the value of $b$ .

[2]

Markscheme / solution

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

$a = 1$ A1

$c = 3$ A1

[2 marks]

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]

Examiners’ report

[N/A]