Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 9 - 2010 - Paper 2
Question 9
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 9 - 2010 - Paper 2
Step 1
y = f(x) + 2
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Answer
For this equation, the graph of f(x) is translated vertically upwards by 2 units. Thus, the maximum point will shift from (−2,5) to (−2,7), while the asymptote will also move from y=1 to y=3. Therefore, the final sketch will show:
Maximum point: (−2,7)
Asymptote: y=3.
Step 2
y = 4f(x)
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Answer
This transformation stretches the graph vertically by a factor of 4. Therefore, the maximum point is scaled from (−2,5) to (−2,20). The asymptote will remain at y=1. On the sketch, include:
Maximum point: (−2,20)
Asymptote: y=1.
Step 3
y = f(x + 1)
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Answer
In this case, the graph of f(x) is translated horizontally to the left by 1 unit. The maximum point moves from (−2,5) to (−3,5), while the asymptote remains unchanged at y=1. The final sketch should depict:
