Figure 1 shows part of the graph of $y = f(x)$, $x \, \in \, \mathbb{R}$. The graph consists of two line segments that meet at the point $R(4, -3)$, as shown in Figure 1. Sketch, on separate diagrams, the graphs of (a) $y = 2f(x+4)$. (b) $y = |f(-x)|$. On each diagram, show the coordinates of the point corresponding to $R$.

A-Level Edexcel Maths Pure Modelling with Exponentials & Logarithms: Figure 1 shows part of the graph

Figure 1 shows part of the graph of $y = f(x)$, $x \, \in \, \mathbb{R}$ - Edexcel - A-Level Maths Pure - Question 5 - 2011 - Paper 3

Question 5

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Figure 1 shows part of the graph of $y = f(x)$, $x \, \in \, \mathbb{R}$. The graph consists of two line segments that meet at the point $R(4, -3)$, as shown in Fi... show full transcript

Worked Solution & Example Answer:Figure 1 shows part of the graph of $y = f(x)$, $x \, \in \, \mathbb{R}$ - Edexcel - A-Level Maths Pure - Question 5 - 2011 - Paper 3

Step 1

(a) $y = 2(f(x+4))$

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Answer

To sketch the graph of $y = 2f(x + 4)$ , perform the following transformations:

Horizontal Shift: Shift the graph of $f(x)$ to the left by 4 units. The point $R(4, -3)$ will now be at $(-1, -3)$ .
Vertical Stretch: Multiply the $y$ -values of the function by 2. So the new $y$ -coordinate of point $(-1, -3)$ will be $2(-3) = -6$ .

In the new sketch, the point corresponding to $R$ is $(-1, -6)$ . The overall shape of the graph remains similar but is vertically stretched.

Step 2

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

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Answer

To sketch the graph of $y = |f(-x)|$ , follow these steps:

Horizontal Reflection: Reflect the graph of $f(x)$ across the $y$ -axis. The point $R(4, -3)$ becomes $(-4, -3)$ .
Apply Absolute Value: Since we take the absolute value of $f(-x)$ , any negative $y$ -values will flip to positive. The $y$ -coordinate of point $(-4, -3)$ will now be transformed to $(-4, 3)$ .

In this sketch, the original point $R$ now appears as $(-4, 3)$ , giving the graph a 'W' shape.

Figure 1 shows part of the graph of $y = f(x)$, $x \, \in \, \mathbb{R}$ - Edexcel - A-Level Maths Pure - Question 5 - 2011 - Paper 3

Worked Solution & Example Answer:Figure 1 shows part of the graph of $y = f(x)$, $x \, \in \, \mathbb{R}$ - Edexcel - A-Level Maths Pure - Question 5 - 2011 - Paper 3

(a) $y = 2(f(x+4))$

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

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