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Pearson Edexcel IAL Mathematics P3.1.4 Combining transformations of functions

Practise combining graph transformations of y=f(x), mapping points, reading ranges and sketching transformed curves from equations.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • find the range after vertical stretches, reflections or translations on a restricted domain
  • sketch transformed graphs with axis intercepts and turning points carried through correctly

P3.1.4 - Combined transformations of functions question 1

[Maximum number: 2]

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

The graph with equation y=f(x) is transformed onto the graph with equation y=af(x+b).
The vertex of the graph with equation y=af(x+b) is (4,20).

Given that a and b are constants, find the value of a and the value of b.

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