Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve crosses the x-axis at the points (2, 0) and (4, 0). The minimum point on the curve is $P(3, -2)$. In separate diagrams sketch the curve with equation (a) $y = -f(x)$ (b) $y = f(2x)$. On each diagram, give the coordinates of the points at which the curve crosses the x-axis, and the coordinates of the image of $P$ under the given transformation.

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

Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 7 - 2005 - Paper 2

Question 7

Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve crosses the x-axis at the points (2, 0) and (4, 0). The minimum point on the curve is $P(3, ... 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 7 - 2005 - Paper 2

Step 1

(a) y = -f(x)

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Answer

To sketch the curve of $y = -f(x)$ :

Reflect the Original Curve: This transformation reflects the original curve across the x-axis. Therefore, all points on the curve will have their y-coordinates changed in sign.
Identify x-axis Intersections: The curve originally crossed the x-axis at (2, 0) and (4, 0), and these points remain the same after reflection.
Determine New Point for P: The point $P(3, -2)$ will now be reflected to $P(3, 2)$ .
Label Important Points: Label the points (2, 0) and (4, 0), as well as the new image of P, which is (3, 2).

Step 2

(b) y = f(2x)

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Answer

To sketch the curve of $y = f(2x)$ :

Stretch the Curve: This transformation stretches the curve horizontally by a factor of 1/2. This will compress the x-coordinates of all points.
Identify New x-axis Intersections: The original intersections of the curve at (2, 0) and (4, 0) will be transformed to (1, 0) and (2, 0) respectively, as follows:
- For the point (2, 0), we find $f(2 imes 1) = f(2)$ giving (1, 0).
- For the point (4, 0), we find $f(2 imes 2) = f(4)$ giving (2, 0).
Determine New Point for P: The original point $P(3, -2)$ will be transformed to $P(1.5, -2)$ , since $x = 3$ maps to $x = rac{3}{2} = 1.5$ .
Label Important Points: Label the points (1, 0) and (2, 0), along with the new image of P, which is (1.5, -2).

Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 7 - 2005 - Paper 2

Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 7 - 2005 - Paper 2

(a) y = -f(x)

(b) y = f(2x)

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