Question

(a) The graph ofy =f(x) is shown. Graph y = 2f (x). (b) The graph of y = g (x) is shown. Graph y =g (2x) Part (a) Part (b) ? ? X

Answer 1

a) The graph of y = 2f(x) can be obtained by vertically stretching the graph of y = f(x) by a factor of 2.

The coordinates of the points on the graph of y = f(x) are (-2, -2) , (0,-3) and (2,-4)

The corresponding points on the graph of y = 2f(x) can be obtained by multiplying the y-coordinates of the above points by 2.

Therefore,

The coordinates of the corresponding points on the graph of  y = 2f(x) are (-2,-4), (0,-6) and (2,-8)

The graph of y = 2f(x) is as below:

6 -6 -8 8 CO

b) The graph of y = g(2x) can be obtained by horizontally compressing the graph of y = g(x) by a factor of 2.

The coordinates of the points on the graph of y = g(x) are (0, 0) , (2,-4) and (4,-2)

The corresponding points on the graph of y = g(2x) can be obtained by dividing the x-coordinates of the above points by 2.

Therefore,

The coordinates of the corresponding points on the graph of  y = g(2x) are (0,0), (1,-4) and (2, -2)

The graph of y = g(2x) is as below:

6 2 -2 -6 -8 -2 -4 -6 -8