21M.1.SL.TZ1.1

pestleMathematicsAASLPaper 121M· sl-2-5-composite-functions-identity-finding-inverse, sl-2-11-transformation-of-functionssource ↗

The graph of $y = f (x)$ for $- 4 \leq x \leq 6$ is shown in the following diagram.

Write down the value of $f (2)$ .

[1]

a.i.

Write down the value of $(f \circ f) (2)$ .

[1]

a.ii.

Let $g (x) = \frac{1}{2} f (x) + 1$ for $- 4 \leq x \leq 6$ . On the axes above, sketch the graph of $g$ .

[3]

Markscheme / solution

$f (2) = 6$ A1

[1 mark]

a.i.

$(f \circ f) (2) = - 2$ A1

[1 mark]

a.ii.

M1A1A1

Note: Award M1 for an attempt to apply any vertical stretch or vertical translation, A1 for a correct horizontal line segment between $- 4$ and $0$ (located roughly at $y = 3$ ),
A1 for a correct concave down parabola including max point at $(2, 4)$ and for correct end points at $(0, 3)$ and $(6, 0)$ (within circles). Points do not need to be labelled.

[3 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]