Photo AI
Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 7 - 2016 - Paper 1
Question 7
Figure 1 shows a sketch of part of the curve with equation $y = f(x)$. The curve has a maximum point A at $(-2, 4)$ and a minimum point B at $(3, -8)$ and passes thr... show full transcript
Worked Solution & Example Answer:Figure 1 shows a sketch of part of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 7 - 2016 - Paper 1
Step 1
(a) $y = 3f(x)$
Answer
To sketch the graph of , we observe that the point A will be scaled vertically.
-
Starting from point A at , after scaling, the new maximum point will be at:
-
Similarly, for point B at , the point will be transformed to:
-
The curve will retain its shape but will stretch vertically by a factor of 3.
-
Mark the new points A' and B' on the graph along with the original points to display the maximum and minimum points clearly, as well as ensuring that the curve crosses the y-axis at (0,0).
Step 2
(b) $y = f(x) - 4$
Answer
For the graph of , we will translate the entire graph of downwards by 4 units:
-
Starting from point A at , after translation, the new maximum point will be:
-
Point B will also move downwards:
-
The curve's shape stays the same; it just shifts down 4 units.
-
Clearly mark the new points A' and B' on the graph and note where the curve crosses the y-axis at (0, -4).