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Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 5 - 2008 - Paper 1
Question 5
Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve passes through the point $(0, 7)$ and has a minimum point at $(7, 0)$. On separate diagrams... 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 5 - 2008 - Paper 1
Step 1
a) $y = f(x) + 3$
Answer
To sketch the curve , we need to understand how the transformation affects the original curve. This equation represents a vertical shift of the original curve upwards by 3 units.
Minimum Point
The minimum point of the original curve is at . After the vertical shift, the new minimum point will be at:
-Intercept
The original curve crosses the -axis at . After the transformation, the new -intercept becomes:
Sketch
Draw a U-shaped curve that passes through with a minimum point at .
Step 2
b) $y = f(2x)$
Answer
The equation represents a horizontal compression of the original curve by a factor of 2. This means that all values of the original function will be halved.
Minimum Point
The original minimum point is at . After compression, the new minimum point will be at: ext{New Minimum Point: } ext{( } rac{7}{2}, 0 ext{ )} = (3.5, 0)
-Intercept
The original curve crosses the -axis at . Since does not alter the -intercept, the curve still crosses the -axis at:
Sketch
Draw a U-shaped curve that touches the -axis at and has a minimum point at .