EXN.1.AHL.TZ0.8

pestleMathematicsAIHLPaper 1EXN· ahl-2-8-transformations-of-graphs-composite-transformationssource ↗

Let $f (x) = a \cos (b (x - c)), a, b, c \in ℝ^{+}$ .

Part of the graph of $y = f (x)$ is shown below. Point $A$ is a local maximum and has coordinates $(1, 3)$ and point $B$ is a local minimum with coordinates $(2, - 3)$ .

Write down a sequence of transformations that will transform the graph of $y = \cos x$ onto the graph of $y = f (x)$ .

Markscheme / solution

Vertical stretch, scale factor $3$ A1

Horizontal stretch, scale factor $\frac{1}{π} \approx 0.318$ A1

Horizontal translation of $1$ unit to the right A1

Note: The vertical stretch can be at any position in the order of transformations. If the order of the final two transformations are reversed the horizontal translation is $π$ units to the right.

[3 marks]

Examiners’ report

[N/A]