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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 \(g(x)\).

[2]
a.

State the equations of the asymptotes of the graph of \(g\).

[2]
b.

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]

a.

\(x =  - 3\)     A1

\(y = 1\)     A1

[2 marks]

Total [4 marks]

b.

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.

a.

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.

b.

Syllabus sections

Topic 2 - Core: Functions and equations » 2.3 » Transformations of graphs: translations; stretches; reflections in the axes.

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