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Pearson Edexcel IAL Mathematics P3.1.3 modulus function

Practise sketching and solving with modulus functions, using vertices, intercepts, inequalities and reflected graph sections from |f(x)|.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • sketch y=|ax+b| or y=|f(x)|, marking vertices, intercepts and asymptotes where relevant
  • solve modulus equations or inequalities by choosing the correct linear branch boundaries
  • use given points on a modulus graph to find constants in equations

P3.1.3 - modulus function question 1

[Maximum number: 6]

Figure 1 shows a sketch of part of the graph with equation y=f(x), where

f(x)=∣3x−13∣+5,x∈Rf(x)=|3x-13|+5,\qquad x\in\mathbb{R}

The vertex of the graph is at point P, as shown in Figure 1.

Figure 1

Figure 1

Question (a)

(a)

State the coordinates of P.

[ 2 ]

Question (b)

(b)

Solve, using algebra and showing your working,

16-2x>|3x-13|+5
[ 4 ]
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