Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2006  January  Q#6
Hits: 66
Question
Figure 1 shows a sketch of the curve with equation y=f(x). The curve passes through the points (0,3) and (4,0) and touches the xaxis at point (1,0).
On separate diagrams sketch the curve with equation
a. y=f(x+1),
b. y=2f(x),
c.
On each diagram show clearly the coordinates of all the points where the curve meets the axes.
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
the positive ydirection.
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 
Value of 
Effect 

Function 


– 
‘Stretch’ 

Coordinates 



Function 



Expansion 

Coordinates 



Function 


Shrinking 

Coordinates 



Function 



Expansion 

Coordinates 



Function 


Shrinking 

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 the original given function whereas all the ycoordinates will be double the original given function.
It is shown in the figure below.
c.
We are given the sketch of the curve with equation;
We are required to sketch the curve of equation;
We know that
Original 
Transformed 
Value of 
Effect 

Function 


– 
‘Stretch’ 
Coordinates 



Function 



Shrinking 
Coordinates 



Function 


Expansion 

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 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 the original given function whereas all the xcoordinates will be ‘c’ times the original given function.
It is shown in the figure below.
Comments