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Date November 2017 Marks available 3 Reference code 17N.1.sl.TZ0.3
Level SL only Paper 1 Time zone TZ0
Command term Sketch Question number 3 Adapted from N/A

Question

The following diagram shows the graph of a function \(f\), with domain \( - 2 \leqslant x \leqslant 4\).

N17/5/MATME/SP1/ENG/TZ0/03

The points \(( - 2,{\text{ }}0)\) and \((4,{\text{ }}7)\) lie on the graph of \(f\).

Write down the range of \(f\).

[1]
a.

Write down \(f(2)\);

[1]
b.i.

Write down \({f^{ - 1}}(2)\).

[1]
b.ii.

On the grid, sketch the graph of \({f^{ - 1}}\).

[3]
c.

Markscheme

correct range (do not accept \(0 \leqslant x \leqslant 7\))     A1     N1

eg\(\,\,\,\,\,\)\([0,{\text{ }}7],{\text{ }}0 \leqslant y \leqslant 7\)

[1 mark]

a.

\(f(2) = 3\)     A1     N1

[1 mark]

b.i.

\({f^{ - 1}}(2) = 0\)     A1     N1

[1 mark]

b.ii.

N17/5/MATME/SP1/ENG/TZ0/03.c/M     A1A1A1     N3

 

Notes:     Award A1 for both end points within circles,

A1 for images of \((2,{\text{ }}3)\) and \((0,{\text{ }}2)\) within circles,

A1 for approximately correct reflection in \(y = x\), concave up then concave down shape (do not accept line segments).

 

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.

Syllabus sections

Topic 2 - Functions and equations » 2.2 » The graph of a function; its equation \(y = f\left( x \right)\) .
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