Photo AI
Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 8 - 2005 - Paper 2
Question 8
Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve crosses the x-axis at the points (2, 0) and (4, 0). The minimum point on the curve is $P(3, ... show full transcript
Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 8 - 2005 - Paper 2
Step 1
Sketch the curve with equation $y = -f(x)$
Answer
-
Reflect the original curve in the x-axis. This means that all points on the original curve will change to .
-
Identify the x-axis intersections from the original graph at points (2, 0) and (4, 0); these will remain the same for the reflected curve.
-
Since the minimum point on the original curve is reflected upwards, the new coordinates of this point will be .
-
The final curve will intersect the x-axis at points (2, 0) and (4, 0), with the image of at (3, 2).
Step 2
Sketch the curve with equation $y = f(2x)$
Answer
-
This transformation represents a horizontal compression of the curve by a factor of 2. Each x-coordinate will be halved, meaning all points shift closer to the y-axis.
-
For the x-axis crossings, the new points will be found by setting the original x-intercepts to half their values: (2, 0) becomes (1, 0) and (4, 0) becomes (2, 0).
-
The minimum point transforms to the new point .
-
The new x-axis intercepts will be (1, 0) and (2, 0), with the image of at (1.5, -2).