The question is as follows:

Complete the table of values and plot the transformed points to obtain the graph of y=-2(-1/3(x+2))^{2}-4

Y=f(x) Y=f(-1/3x) Y=-2f(-1/3x) Y=-2f(-1/3(x+2)) ^{2}-4(0,0) (1,1) (2,4) (3,9)

I am supposed to find out the transformed x and y values for the function f(x) for Y=f(- 1/3x), etc., as per the table above.

I just want to mention that I am NOT plugging the (0,0), (1,1) etc. values into the equations given, but that they correspond to the transformation of the basic equation y=f(x).

I have no clue at all how to tackle this, and any help with the answer, as well as some insight into what is going on here, would be greatly appreciated.

Thanks.

Oh, also, the previous questions in this part of my homework were as follows (I am only jotting them down here because the above question is part c of a three part question and I'm worried the other parts may be relevant.

a)State the base function that corresponds to the transformed function y = -2(-1/3(x+2))^{2}-4

a) f(x)=x^{2}

b)State the parameters and describe the corresponding transformations.

b)

a = -2 | Stretched vertically and reflected in the x axis by a factor of 2

k = -1/3 | reflected in the y axis and horizontally stretched by a factor of -1/3

d= -2 shifted 2 units left