Figure 1 shows a sketch of the graph of $y = f(x)$. The graph intersects the $y$-axis at the point $(0, 1)$ and the point $A(2, 3)$ is the maximum turning point. Sketch, on separate axes, the graphs of (i) $y = f(-x) + 1$, (ii) $y = f(x + 2) + 3$, (iii) $y = 2f(2x)$. On each sketch, show the coordinates of the point at which your graph intersects the $y$-axis and the coordinates to which $A$ is transformed.

Photo AI

Figure 1 shows a sketch of the graph of $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 8 - 2010 - Paper 2

Question 8

Figure 1 shows a sketch of the graph of $y = f(x)$. The graph intersects the $y$-axis at the point $(0, 1)$ and the point $A(2, 3)$ is the maximum turning point. S... show full transcript

Worked Solution & Example Answer:Figure 1 shows a sketch of the graph of $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 8 - 2010 - Paper 2

Step 1

y = f(-x) + 1

96%

114 rated

Answer

The graph of $y = f(-x) + 1$ will be a reflection of the original graph across the $y$ -axis, translated up by 1 unit.

The intersection with the $y$ -axis occurs at:

$(0, 2)$

The point $A(2, 3)$ is transformed to:

$A'(-2, 4)$

Step 2

y = f(x + 2) + 3

99%

104 rated

Answer

The equation $y = f(x + 2) + 3$ translates the graph left by 2 units and up by 3 units.

The intersection with the $y$ -axis occurs at:

$(0, 6)$

The point $A(2, 3)$ is transformed to:

$A'(0, 6)$

Step 3

y = 2f(2x)

96%

101 rated

Answer

For the equation $y = 2f(2x)$ , the graph undergoes a horizontal compression by a factor of 2 and a vertical stretch by a factor of 2.

The intersection with the $y$ -axis occurs at:

$(0, 2)$

The point $A(2, 3)$ is transformed to:

$A'(1, 6)$

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

;