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. On separate diagrams, sketch the curve with equation (a) $y = f(x) + 2$ (b) $y = 4f(x)$ (c) $y = f(x) + 1$ On each diagram, show clearly the coordinates of the maximum point and the equation of the asymptote.

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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. On ... show full transcript

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

a) $y = f(x) + 2$

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Answer

To sketch the curve for $y = f(x) + 2$ , shift the original graph of $f(x)$ vertically upwards by 2 units.

The new maximum point becomes $(-2, 5 + 2) = (-2, 7)$ .

The equation of the asymptote also shifts similarly. As the original asymptote $y = 1$ goes up by 2, it now becomes $y = 3$ .

Step 2

b) $y = 4f(x)$

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Answer

The graph of $y = 4f(x)$ involves stretching the function vertically by a factor of 4.

The maximum point, originally at $(-2, 5)$ , will now be at $(-2, 4 imes 5) = (-2, 20)$ .

The horizontal asymptote will remain at $y = 1$ .

Step 3

c) $y = f(x) + 1$

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Answer

To sketch the curve for $y = f(x) + 1$ , shift the original graph vertically upwards by 1 unit.

The new maximum point becomes $(-2, 5 + 1) = (-2, 6)$ .

The asymptote is $y = 1$ , which remains unchanged.

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