Figure 1 shows a sketch of the curve C with equation $y = f(x)$. There is a maximum at $(0, 0)$, a minimum at $(2, -1)$ and C passes through $(3, 0)$. On separate diagrams sketch the curve with equation a) $y = f(x + 3)$. b) $y = f(-x)$. On each diagram show clearly the coordinates of the maximum point, the minimum point and any points of intersection with the $x$-axis.

A-Level Edexcel Maths Pure Differentiation: Figure 1 shows a sketch of the c

Figure 1 shows a sketch of the curve C with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2009 - Paper 1

Question 6

Figure 1 shows a sketch of the curve C with equation $y = f(x)$. There is a maximum at $(0, 0)$, a minimum at $(2, -1)$ and C passes through $(3, 0)$. On separate di... show full transcript

Worked Solution & Example Answer:Figure 1 shows a sketch of the curve C with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2009 - Paper 1

Step 1

a) $y = f(x + 3)$

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Answer

To sketch the curve $y = f(x + 3)$ , we apply a horizontal shift to the left by 3 units. This means the maximum point at $(0, 0)$ will shift to $(-3, 0)$ , and the minimum point at $(2, -1)$ will shift to $(-1, -1)$ .

The general shape will remain the same, resembling the original graph but shifted. The $x$ -intercepts will also reflect this shift: if the original curve passes through $(3, 0)$ , it will now pass through $(0, 0)$ . Hence, we will mark all necessary points on the new axes.

Maximum point: $(-3, 0)$
Minimum point: $(-1, -1)$
Intersection points: $(-3, 0)$ and $(0, 0)$

Step 2

b) $y = f(-x)$

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Answer

For the sketch of $y = f(-x)$ , we perform a reflection about the $y$ -axis. The maximum point originally at $(0, 0)$ remains in the same position. The minimum point at $(2, -1)$ will shift to $(-2, -1)$ . The point $(3, 0)$ will now reflect to $(-3, 0)$ .

Therefore, the key points to note are:

Maximum point: $(0, 0)$
Minimum point: $(-2, -1)$
Intersection points: $(0, 0)$ and $(-3, 0)$

Figure 1 shows a sketch of the curve C with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2009 - Paper 1

Worked Solution & Example Answer:Figure 1 shows a sketch of the curve C with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2009 - Paper 1

a) $y = f(x + 3)$

b) $y = f(-x)$

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