Figure 2 shows part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2012 - Paper 5
Question 6
Figure 2 shows part of the curve with equation $y = f(x)$.
The curve passes through the points $P(-1.5, 0)$ and $Q(0, 5)$ as shown.
On separate diagrams, sketch the... show full transcript
Worked Solution & Example Answer:Figure 2 shows part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2012 - Paper 5
Step 1
Sketch the curve with equation $y = f(-x)$
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Answer
The reflection of the curve across the y-axis. The point P(-1.5, 0) becomes P'(1.5, 0), and Q(0, 5) remains the same. The curve retains its shape but is symmetric about the y-axis.
Step 2
Sketch the curve with equation $y = f(|x|)$
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Answer
This represents the reflection of the portion of the curve in the first quadrant across the y-axis. The graph includes points at (0, 5) and exhibits symmetry. The curve at y=0 intersects at (0.5,0).
Step 3
Sketch the curve with equation $y = 2f(3x)$
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Answer
The graph of y=f(3x) compresses the graph horizontally by a factor of 3. The points (1.0, 10) and (-0.5, 0) will be the new coordinates reflecting this transformation. The curve's shape will expand vertically by a factor of 2.
