Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2013  June  Q#8
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Question
Figure 1 shows a sketch of the curve with equation y = f(x) where
,
The curve crosses the xaxis at (1, 0), touches it at (–3, 0) and crosses the yaxis at (0, –9).
a. In the space below, sketch the curve C with equation y=f(x+2) and state the coordinates of the points where the curve C meets the xaxis.
b. Write down an equation of the curve C.
c. Use your answer to part (b) to find the coordinates of the point where the curve C meets the y axis.
Solution
a.
We are given sketch of the curve and are required to sketch the graph of the curve .
We are given the sketch of the curve with equation;
We are required to sketch the curve of equation;
Translation through vector transforms the graph of into the graph of .
Transformation of the function into results from translation through vector .
Translation through vector represents the move, units in the positive xdirection and units in the positive ydirection.
Original 
Transformed 
Translation Vector 
Movement 

Function 



units in units in 
Coordinates 


However, for the given case we consider following.
Translation through vector represents the move, units in the negative xdirection and units in the ydirection.
Translation through vector transforms the function into .
Transformation of the function into results from translation through vector .
Translation through vector transforms the function into which means shift towards left along xaxis.
Original 
Transformed 
Translation Vector 
Movement 

Function 



units in 
Coordinates 


It is evident that we are required to transform the function into , therefore it is case of translation of along negative xaxis by 2 unit.
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, red one is the original while orange is the transformed graph.
b.
We are given;
We are can write the equation of the curve C by replacing x with x+2;
c.
We are required to find the coordinates of the point where the curve C meets the yaxis. We are looking for yintercept of the curve C.
The point at which curve (or line) intercepts yaxis, the value of . So we can find the value of coordinate by substituting in the equation of the curve (or line).
We have found in (b) equation of the curve C;
Substitute x=0;
Hence, coordinates of yintercept of the curve C are (0,25).
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