Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 5 - 2008 - Paper 6
Question 5
Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve passes through the origin $O$ and the points $A(5, 4)$ and $B(-5, -4)$.
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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 6
Step 1
y = |f(x)|
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Answer
To sketch the graph of y=∣f(x)∣, maintain the portion of the curve that is above the x-axis and reflect any part that is below the x-axis across the x-axis. The points remain as follows:
Point A remains at (5, 4).
Point B, which was originally at (-5, -4), becomes (-5, 4) after reflection.
Step 2
y = f(|x|)
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Answer
For the graph of y=f(∣x∣), reflect the portion of the graph for x>0 (the right side) to the left side of the y-axis. The graph will be symmetrical about the y-axis. The points are:
Point A at (5, 4)
Point B at (-5, -4) remains unchanged as it mirrors the portion from the right side.
Step 3
y = 2f(x + 1)
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Answer
To sketch y=2f(x+1), shift the entire graph of f(x) one unit to the left, and then stretch it vertically by a factor of 2. The coordinates of the relevant points become:
Point A changes to (4, 8) after the transformation.
Point B translates to (-6, -8), reflecting its vertical stretching and horizontal shift.
