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 6 - 2008 - Paper 6

Question 6

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 diagr... 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 6 - 2008 - Paper 6

Step 1

y = |f(x)|

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Answer

For the graph of $y = |f(x)|$ , the original curve is reflected in the x-axis where it is below the x-axis. The points $A(5, 4)$ and $B(-5, -4)$ will change.

The point $A(5, 4)$ remains the same.
The point $B(-5, -4)$ translates to $(-5, 4)$ .

Therefore, the new coordinates are $A(5, 4)$ and $B(-5, 4)$ .

Step 2

y = f(|x|)

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Answer

For the graph of $y = f(|x|)$ , the right part of the graph will mirror over the y-axis.

Thus, the point $A(5, 4)$ remains unchanged, while point $B(-5, -4)$ is unwarranted and will correspond to the reflection of $A(5, 4)$ .

Therefore, the new coordinates are $A(5, 4)$ and $B(5, 4)$ .

Step 3

y = 2f(x + 1)

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Answer

In the case of $y = 2f(x + 1)$ , the graph of $f(x)$ shifts to the left by 1 unit and is scaled vertically by a factor of 2.

The point $A(5, 4)$ translates to $(4, 8)$ after doubling the y value.
The point $B(-5, -4)$ translates to $(-6, -8)$ after shifting left and doubling.

The new coordinates are $A(4, 8)$ and $B(-6, -8)$ .

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