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Solution of Past Paper of CAIE Math 9709/12 Feb/Mar 2020 Question # 2 $2.99   Add to cart

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Solution of Past Paper of CAIE Math 9709/12 Feb/Mar 2020 Question # 2

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This document presents most carefully worked out and thoroughly explained complete Solution of Past Paper of Cambridge AS/A Level Mathematics (9709), Pure Mathematics 1, Feb/March 2020 We also provide on-on-one online help for students who still need some help beyond our provided solution. We al...

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  • October 21, 2023
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  • 2023/2024
  • Exam (elaborations)
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CIE/GCE/AS/Math/P1/20/Mar/12/Q#2

Question
1
The graph of 𝑦 = 𝑓(𝑥 ) is transformed to the graph of 𝑦 = 1 + 𝑓 ( 𝑥).
2

Describe fully the two single transformations which have been combined to give the
resulting transformation.


Solution

We are given function;
𝑦 = 𝑓 (𝑥 )


The following function represents the vertical translation (along y-axis) of graph by 𝑘
units upwards;

𝑦 = 𝑓(𝑥 ) + 𝑘

Therefore, for the given case, following will represent vertical translation (along y-axis)
of graph by 1 unit upwards;

𝑦 = 1 + 𝑓 (𝑥 )

The following function represents the horizontal stretch (along x-axis) of graph by a
factor of 𝑘 if 0 < |𝑘| < 1;

𝑦 = 𝑓(𝑘𝑥 )

Therefore, for the given case, following will represent horizontal stretch (along x-axis)
1
of graph by a factor of ;
2
1
𝑦 = 𝑓 ( 𝑥)
2
1
Hence, the function 𝑦 = 1 + 𝑓 ( 𝑥) is obtained by following two transformation of 𝑦 =
2
𝑓(𝑥 );

• Vertical translation (along y-axis) of graph by 1 unit upwards

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