A-LevelMathematicsFunctions9709/12 · Feb/Mar 2023 · Q24 Marks

A function f is defined by f(x) = x² – 2x + 5 for x ∈ R. A sequence of transformations is applied in the following order to the graph of y = f(x) to give the graph of y = g(x). Stretch parallel to the x-axis with scale factor ½ Reflection in the y-axis Stretch parallel to the y-axis with scale factor 3 Find g(x), giving your answer in the form ax² + bx + c, where a, b and c are constants.

(a)Find g(x), giving your answer in the form ax² + bx + c, where a, b and c are constants.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

[M1] Stretch: (2x)²-2(2x)+5 or (x−1)² + 4 leading to (2x-1)² +4 Replacing x by 2x.
[M1] Reflection: (-2x)²-2(-2x)+5 or (-2x−1)² +4 Replacing x by – x. FT on their stretch.
[M1] Stretch: 3{(-2x)²-2(-2x)+5} or 3{(-2x−1)²+4} Multiplying the whole function by 3. FT on their (stretch plus reflection).
[A1] 12x² +12x+15

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Topic: Functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Feb/Mar 2023 Paper 1 Variant 2, question 2.

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