Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve passes through the origin O and through the point (6, 0). The maximum point on the curve is (3, 5). On separate diagrams, sketch the curve with equation (a) $y = 3f(x)$. (b) $y = f(x + 2)$. On each diagram, show clearly the coordinates of the maximum point and of each point at which the curve crosses the $x$-axis.

Photo AI

Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2005 - Paper 1

Question 6

Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve passes through the origin O and through the point (6, 0). The maximum point on the curve is ... 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 6 - 2005 - Paper 1

Step 1

(a) $y = 3f(x)$

96%

114 rated

Answer

To sketch the curve for the equation $y = 3f(x)$ :

Start by noting that scaling the function $f(x)$ vertically by a factor of 3 will stretch the curve vertically.
The maximum point of the original function $f(x)$ is at (3, 5). After applying the scaling, the new maximum point will be at (3, 15).
The curve will still cross the $x$ -axis at the same points: (0, 0) and (6, 0).
Ensure the shape of the graph remains smooth and rounded, reflecting the vertical stretch.

Step 2

(b) $y = f(x + 2)$

99%

104 rated

Answer

For the equation $y = f(x + 2)$ :

This transformation shifts the graph of the function to the left by 2 units.
Therefore, the maximum point (3, 5) will now be at (1, 5).
The $x$ -intercepts will also shift: the new $x$ -intercepts are now at (-2, 0) and (4, 0).
Again, maintain the curved shape of the graph, clearly marking the new maximum point and intercepts on the sketch.

Join the A-Level students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;