CAIE A-Level Mathematics AS Economics: Policies for Current Account Imbalances

[Maximum number: 6]

Figure for Question CAIE A-Level Mathematics AS 1.2.5 Graph Transformations Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the graph of y=f(x) where the function f is defined by

f(x)=3+2 \sin \frac{1}{4} x \text { for } 0 \leqslant x \leqslant 2 \pi .

Describe fully a sequence of three transformations which can be combined to transform the graph of $y=\sin x$ for $0 \leqslant x \leqslant \frac{1}{2} \pi$ to the graph of y=f(x), making clear the order in which the transformations are applied.

\{ \ indicates different elements throughout.}

\{Stretch\} \{factor 4\} \{in x-direction\}

B2, 1,
0

B2 for fully correct, B1 with two elements correct.
Condone use of 'sf' instead of factor and 'co-ordinates'
stretched instead of graph stretched.

Marking guidance:

Allow any mention of x-axis, horizontally or y-axis
invariant.
Wavelength or period increased by a factor of 4 for B2 or
by 4 for B1 .

\{Stretch\} \{factor 2\} \{in y-direction\}

B2, 1,
0

B2 for fully correct, B1 with two elements correct.
Condone use of 'sf' instead of factor and 'co-ordinates'
stretched instead of graph stretched.
Allow any mention of y-axis, vertically or x-axis invariant.
Allow y 'co-ordinates' doubled or amplitude doubled for
$\{$ Translation $\}\binom{\{0\}}{\{3\}}$

B2, 1,
0

B2 for fully correct, B1 with two elements correct.
Allow shift. Any mention of y axis, y-direction or
vertically implies $\{0\}$ , so shift by 3 vertically is B2 , but
shift by a factor of 3 vertically or a translation of 3 'up' is
6

After scoring B2, B2 the final transformation can only be awarded B2 if the order is fully correct i.e. the translation
must not be applied before the y stretch. If all correct except the order award B2B2B1.

CAIE A-Level Mathematics AS 1.2.5 Graph Transformations Questions question 1