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
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
