Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 10 - 2010 - Paper 2
Question 10
Figure 1 shows a sketch of part of the curve with equation $y = f(x)$.
The curve has a maximum point $(-2, 5)$ and an asymptote $y = 1$, as shown in Figure 1.
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Worked Solution & Example Answer:Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 10 - 2010 - Paper 2
Step 1
a) $y = f(x) + 2$
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Answer
To sketch the graph of y=f(x)+2, we translate the original graph f(x) vertically upwards by 2 units. This means that the maximum point will now be at (−2,7) instead of (−2,5). The equation of the asymptote will shift as well, resulting in the new asymptote y=3. Therefore, the diagram should include the maximum point coordinates (−2,7) and the asymptote equation y=3.
Step 2
b) $y = 4f(x)$
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Answer
Here, the graph of y=4f(x) results from a vertical stretch of the original function by a factor of 4. The maximum point will move from (−2,5) to (−2,20). However, the asymptote remains unchanged at y=1, since vertical stretching does not affect the horizontal asymptote. The sketch must clearly indicate the maximum point coordinates (−2,20) and the asymptote equation y=1.
Step 3
c) $y = f(x + 1)$
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Answer
For the equation y=f(x+1), we apply a horizontal translation of the graph to the left by 1 unit. Consequently, the maximum point shifts from (−2,5) to (−3,5), as the asymptote remains at y=1. The diagram should display the maximum point coordinates (−3,5) and the asymptote equation y=1.
