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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 diagram... 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
y = f(x + 3)
Answer
To sketch the curve , recognize that this represents a horizontal shift of the original function to the left by 3 units.
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Plot Key Points:
- The maximum point (0, 0) shifts to (-3, 0).
- The minimum point (2, -1) shifts to (-1, -1).
- The point (3, 0) shifts to (0, 0).
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Identify x-axis Intersections:
- The curve intersects the x-axis at the new points, which are clearly derived from the transformations applied.
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Draw the Curve:
- The curve should maintain its shape but shifted left. It will touch the x-axis at (-3, 0) and (-1, 0) as appropriate.
Step 2
y = f(-x)
Answer
To sketch the curve , this represents a reflection of the original function across the y-axis.
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Plot Key Points:
- The maximum point (0, 0) remains unchanged, so it is still at (0, 0).
- Reflect the minimum point (2, -1) to (-2, -1).
- The curve goes through the reflected point: (3, 0) to (-3, 0).
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Identify x-axis Intersections:
- The new intersections with the x-axis will also reflect the appropriate transformations.
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Draw the Curve:
- Ensure to accurately reflect the changing behavior near the min and max points while maintaining the curve's overall shape.