Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2011  January  Q#5
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Question
Figure 1 shows a sketch of the curve with equation y = f (x) where
,
The curve passes through the origin and has two asymptotes, with equations y=1 and x=2, as shown in Figure.
a. In the space below, sketch the curve with equation y = f (x −1) and state the equations of the asymptotes of this curve.
b. Find the coordinates of the points where the curve with equation y = f (x −1) crosses the coordinate 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
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 positive xaxis of original given function.
Same would be effect on equations of asymptotes. The x=2 will translate to x=3 whereas y=1 will remain unchanged.
It is shown in the figure below.
b.
We are given the sketch of the curve with equation;
The equation for
Therefore equation will be;
As demonstrated in (a), the horizontal translation of y=f(x) to y=f(x1), along positive xaxis by unit 1, will translate xintercept of the curve from origin (0,0) to (1,0).
We need to find yintercept.
The point
Therefore;
Hence, coordinates of yintercept are
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