Question 1

Paper 2, calculatorMedium7 marks

Figure 1 shows the graph of y=f(x)y=f(x) for −4≤x≤4-4\leq x\leq 4

-5-4-3-2-112345-4-3-2-10123456xyf(x)

The graph of y=g(x)y=g(x) is obtained from the graph of y=f(x)y=f(x) by reflecting it in the xx-axis, applying a vertical stretch with scale factor 22 and then translating it 11 unit upwards.

(a)

Write down f(−2)f(-2)

[1]
(b)

On the same axes as Figure 1, sketch the graph of y=g(x)y=g(x) Mark the image of the point on y=f(x)y=f(x) for which x=−2x=-2

[2]
(c)

Using Figure 1, determine all values of xx for which g(x)=3g(x)=3

[2]
(d)

For the point (−2,2)(-2,2) on y=f(x)y=f(x) determine its image ordinate if the translation upwards by 11 unit is performed after the reflection but before the vertical stretch. Hence state whether this order of transformations gives the same graph as y=g(x)y=g(x)

[2]

More AA 2.4 Transformations of graphs questions