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). In separate diagrams, sketch the graph with equation a) $y = |f(x)|$, b) $y = f(|x|)$, c) $y = 2f(x + 1)$. On each sketch, show the coordinates of the points corresponding to A and B.

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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 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). In 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 5 - 2008 - Paper 6

Step 1

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

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Answer

To sketch the graph of $y = |f(x)|$ , we take the graph of $f(x)$ and reflect any parts below the x-axis upwards. The coordinates of point A remain (5, 4), while point B at (-5, -4) will be reflected to (-5, 4).

Thus, the graph will have points:

A(5, 4)
B(-5, 4)

Step 2

b) $y = f(|x|)$

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Answer

In this case, we will take the graph of $f(x)$ and reflect it across the y-axis for the negative side of the x-axis. As a result, the graph will look the same as the right side for the left side. Here, the coordinates for both points A and B will be:

A(5, 4)
B(-5, -4),

indicating that B remains at (-5, -4) on both sides.

Step 3

c) $y = 2f(x + 1)$

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Answer

For this transformation, we first shift the graph of $f(x)$ to the left by 1 unit. Next, we vertically stretch the graph by a factor of 2. The new coordinates of point A will be at (4, 8) after both transformations, and point B at (-6, -8). Thus, we have:

A(4, 8)
B(-6, -8)

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