IBDP Maths AHL 2.16 The graphs of the Mod functions AA HL Paper 2- Exam Style Questions- New Syllabus

Question

The graphs of \(y = |x + 1|\) and \(y = |x – 3|\) are shown below.

Graphs of absolute value functions

Let \(f(x) = |x + 1| – |x – 3|\).

(a) Draw the graph of \(y = f(x)\) on the blank grid below. [4]

Blank grid for graph

(b) Hence state the value of:

(i) \(f'(-3)\);

(ii) \(f'(2.7)\);

(iii) \(\int_{-3}^{-2} f(x)dx\). [4]

▶️ Answer/Explanation

Markscheme

(a) [4 marks]

Graph of y=f(x) M1A1A1A1

(b) [4 marks]

(i) \(f'(-3) = 0\) A1
(ii) \(f'(2.7) = 2\) A1
(iii) Finding area of rectangle M1
\(\int_{-3}^{-2} f(x)dx = -4\) A1

Note: Award M1A0 for the answer 4 (unsigned area).

IBDP Maths AHL 2.16 The graphs of the Mod functions AA HL Paper 2- Exam Style Questions