Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663A/01)  Year 2014  January  Q#4
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Question
Figure 1 shows a sketch of a curve with equation y = f(x).
The curve crosses the yaxis at (0, 3) and has a minimum at P (4, 2).
On separate diagrams, sketch the curve with equation
a. y = f(x + 4),
b. y = 2f(x).
On each diagram show the coordinates of minimum point and any point of intersection with the y axis.
Solution
a.
We are given the sketch of the curve with equation;
We are required to sketch the curve of equation;
Translation through vector
Transformation of the function
Translation through vector
Original 
Transformed 
Translation Vector 
Movement 

Function 




Coordinates 


However, for the given case we consider following.
Translation through vector
Translation through vector
Transformation of the function
Translation through vector
Original 
Transformed 
Translation Vector 
Movement 

Function 




Coordinates 


It is evident that we are required to transform the function
It is also evident from the above table that only xcoordinates of the graph change whereas y coordinates of the graph will remain unchanged.
Hence, the new function has all the ycoordinates same as that of original given function whereas all the xcoordinates are shifted towards negative xaxis of original given function.
It is shown in the figure below.
b.
We are given the sketch of the curve with equation;
We are required to sketch the curve of equation;
We know that


Original 
Transformed 
Effect 

Function 


Expansion 
Coordinates 



Function 


Shrinking 
Coordinates 



Function 


Shrinking 
Coordinates 



Function 


Expansion 
Coordinates 


From the above table, as highlighted, it is evident that we are required to transform the function
Transformation of the function
Expansion of the function
It is also evident from the above table that only ycoordinates of the graph change whereas x coordinates of the graph will remain unchanged.
Hence, the new function has all the xcoordinates same as that of original given function whereas all the ycoordinates are twotimes of original given function.
It is shown in the figure below.
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