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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 $y = f(-x)$
Answer
To reflect the curve across the y-axis, take each point on the original curve and change the sign of the x-coordinate. The key points to plot are:
- Original point becomes
- Original point remains
After sketching, the curve should touch the x-axis at and rise to .
Step 2
Sketch the curve with equation $y = |f(x)|$
Answer
This transformation reflects any portion of the curve that lies below the x-axis to above it, keeping the parts above the x-axis unchanged. The coordinates to indicate are:
- stays as .
- The point where the curve intersects the x-axis at remains the same but any points from the original curve below the x-axis will now be reflected.
Visualize the transformation and draw the new curve, ensuring to display the key points accurately.
Step 3
Sketch the curve with equation $y = 2f(3x)$
Answer
This equation scales the curve vertically by a factor of 2 and compresses it horizontally by a factor of 1/3. For the key coordinates:
- At the original point , the new point will remain at after transformation since is .
- For point , the new point will transform to (as multiplies by ).
- Calculate additional x-intercepts by setting to find further intercepts.
Ensure the sketch reflects these transformations accurately.