IB Questionbank

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 $y = f(x)$ .

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

Using the information on the graph,

Markscheme

$a = 1$ 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

Syllabus sections

Topic 2 - Core: Functions and equations » 2.2 » The graphs of the functions

$y = \left| {f\left( x \right)} \right|$ and

$y = f\left( {\left| x \right|} \right)$ .

18M.1.hl.TZ2.2a: Sketch the graphs of $y = \frac{x}{2} + 1$ and $y = \left| {x - 2} \right|$ on the...
18M.2.hl.TZ2.10c: Sketch the graph of $y = g\left( t \right)$ for t ≤ 0. Give the coordinates of any...
18M.2.hl.TZ2.10b: Show that $g\left( t \right) = {\left( {\frac{{1 + t}}{{1 - t}}} \right)^2}$ .
16M.2.hl.TZ1.5b.ii: Write down the range of $f$ .
16M.2.hl.TZ1.5b.i: Sketch the graph $y = f(x)$ .
16M.1.hl.TZ1.7b: Find the exact solutions to the equation $x + 2 = \left| {\frac{7}{{x - 4}}} \right|$ .
16M.1.hl.TZ1.7a: Sketch on the same axes the curve $y = \left| {\frac{7}{{x - 4}}} \right|$ and the line...
16N.1.hl.TZ0.3a: state the value of $a$ and the value of $c$ ;
17M.1.hl.TZ1.11e: Sketch the graph of $y = f\left( {\left| x \right|} \right)$ .
12M.1.hl.TZ1.2a: Draw the graph of y = f (x) on the blank grid below.

Question

Markscheme

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