# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#8

Question Figure 1 shows a sketch of the curve with equation y = f(x) where , The curve crosses the x-axis at (1, 0), touches it at (–3, 0) and crosses the y-axis 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 x-axis.

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 x-direction and units in  the positive y-direction.

 Original Transformed Translation Vector Movement Function     units in positive x-direction units in positive y-direction Coordinates  However, for the given case we consider following.

Translation through vector represents the move, units in the negative x-direction and units  in the y-direction.

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 x-axis.

 Original Transformed Translation Vector Movement Function    units in negative x-direction Coordinates  It is evident that we are required to transform the function into , therefore it is  case of translation of along negative x-axis by 2 unit.

It is also evident from the above table that only x-coordinates of the graph change whereas y- coordinates of the graph will remain unchanged.

Hence, the new function has all the y-coordinates same as that of original given function whereas  all the x-coordinates are shifted towards negative x-axis 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 y-axis. We are looking for y-intercept of the curve C.

The point at which curve (or line) intercepts y-axis, 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 y-intercept of the curve C are (0,25).