Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 9 - 2006 - Paper 1
Question 9
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 x-axis at the point $(1, 0)$... show full transcript
Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 9 - 2006 - Paper 1
Step 1
a) $y = f(x + 1)$
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Answer
To sketch the graph of y=f(x+1), we shift the original curve one unit to the left. The points that were originally at (0,3), (1,0), and (4,0) will now be at the following coordinates:
(0−1,3)=(−1,3)
(1−1,0)=(0,0)
(4−1,0)=(3,0).
Make sure to indicate these new points clearly on the graph.
Step 2
b) $y = 2f(x)$
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Answer
For the equation y=2f(x), we stretch the original curve vertically by a factor of 2. This means the y-coordinates of our reference points will double:
The point (0,3) becomes (0,6).
The point (1,0) remains (1,0) since it touches the x-axis.
The point (4,0) remains (4,0).
Label the new point at (0,6) clearly, and ensure the vertical stretch is represented on the sketch.
Step 3
c) $y = \frac{1}{2} f(2x)$
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Answer
The equation y=21f(2x) transforms the graph by stretching it horizontally by a factor of rac{1}{2} and vertically compressing it by a factor of rac{1}{2}. Calculate the new coordinates:
The point (0,3) becomes (0,21⋅3)=(0,1.5).
The point (1,0) will now be at (21,0).
The point (4,0) transforms to (2,0).
Ensure you clearly label the points (0,1.5), (21,0), and (2,0) on the diagram.
