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Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 4 - 2008 - Paper 1
Question 4
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, sk... 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 4 - 2008 - Paper 1
Step 1
a) $y = f(x) + 3$
Answer
To sketch the curve represented by , note that this transformation shifts the original curve vertically upwards by 3 units. The minimum point of the original curve is (7, 0), which will now become (7, 3).
To represent the crossing of the curve with the -axis, we find the new -intercept by substituting into the function:
Thus, the curve will now cross the -axis at (0, 10). The sketch will show a U-shape, maintaining the form while ensuring to label the minimum point at (7, 3) and the -intercept at (0, 10) clearly.
Step 2
b) $y = f(2x)$
Answer
This equation represents a horizontal compression of the original curve by a factor of 2. The minimum point originally at (7, 0) will be adjusted to a new location. To find the new minimum point:
- The -coordinate is divided by 2: x_{min} = rac{7}{2} = 3.5
Thus, the new minimum point is now at (3.5, 0).
Next, to find the -intercept, substitute in the function:
The curve crosses the -axis at (0, 7). In the sketch, you should clearly display the new minimum point (3.5, 0) and the crossing point at (0, 7).