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 Exponential & 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

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

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... 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 $y = 2f(x + 4)$ , follow these steps:

Identify the effect of the transformation: The transformation involves a horizontal shift to the left by 4 units and a vertical stretch by a factor of 2.
Shift the original point R: The point $R(4, -3)$ shifts to the left:
- New coordinates become $(4 - 4, -3) = (0, -3)$ .
Apply the vertical stretch: Multiply the y-coordinate by 2:
- New coordinates become $(0, -3 \times 2) = (0, -6)$ .
Sketch the new graph: The transformed graph will still form a V-shape, opening upwards, intersecting the y-axis at $(0, -6)$ .

Step 2

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

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Answer

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

Identify the effect of the transformation: This transformation involves a reflection across the y-axis followed by taking the absolute value of the function, which ensures all values are non-negative.
Reflect the original point R: The point $R(4, -3)$ reflects to $R(-4, -3)$ .
Apply the absolute value: The y-coordinate becomes positive:
- New coordinates become $(-4, |-3|) = (-4, 3)$ .
Sketch the new graph: The resulting graph assumes a W-shape that opens upwards, with vertices at $(-4, 3)$ and meaningful intersections on the x-axis, forming a downward 'V' in quadrants 1 and 2.

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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