Figure 1 shows a sketch of part of the curve with equation $y = f(x)$. The curve has a maximum point A at $(-2, 4)$ and a minimum point B at $(3, -8)$ and passes through the origin O. On separate diagrams, sketch the curve with equation (a) $y = 3f(x)$, (b) $y = f(x) - 4$. On each diagram, show clearly the coordinates of the maximum and the minimum points and the coordinates of the point where the curve crosses the y-axis.

A-Level Edexcel Maths Pure Sequences & Series: Figure 1 shows a sketch of part

Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2016 - Paper 1

Question 6

Figure 1 shows a sketch of part of the curve with equation $y = f(x)$. The curve has a maximum point A at $(-2, 4)$ and a minimum point B at $(3, -8)$ and passes thr... 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 6 - 2016 - Paper 1

Step 1

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

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Answer

To sketch the curve for the equation $y = 3f(x)$ , we need to apply a vertical stretch by a factor of 3 to the original function.

Maximum Point:
- The original maximum point $A$ is at $(-2, 4)$ .
- The new coordinates become:
  - New Maximum $A' = (-2, 3 * 4) = (-2, 12)$ .
Minimum Point:
- The original minimum point $B$ is at $(3, -8)$ .
- The new coordinates become:
  - New Minimum $B' = (3, 3 * -8) = (3, -24)$ .
Crossing the y-axis:
- The original function passes through the origin $(0, 0)$ , and the transformed function also passes through $y = 0$ when $x = 0$ .

The sketch should represent these new points, ensuring the shape maintains the similar curve structure as the original.

Step 2

(b) $y = f(x) - 4$

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Answer

For the equation $y = f(x) - 4$ , we apply a vertical shift downward by 4 units.

Maximum Point:
- The original maximum point $A$ $A$ at $(-2, 4)$ $(- 2, 4)$ becomes:
  - New Maximum $A'' = (-2, 4 - 4) = (-2, 0)$ .
Minimum Point:
- The original minimum point $B$ $B$ at $(3, -8)$ $(3, - 8)$ becomes:
  - New Minimum $B'' = (3, -8 - 4) = (3, -12)$ .
Crossing the y-axis:
- The point where the curve crosses the y-axis remains at $y = 0$ when $x = 0$ . The function will pass through $(0, -4)$ after the downward shift.

The diagram should accurately show the new coordinates, as well as the downward shift in the curve, while retaining the original shape.

Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2016 - Paper 1

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 6 - 2016 - Paper 1

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

(b) $y = f(x) - 4$

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