Stuck on transforming a base function, completing a table of values, and graphing it

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)=x²
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

Completing the table is very easy. What you need to do is just apply the transformations one at a time to the original points of . I am filling the table for you as your reading this!


Edit: Here you go hope this helps you Attachment 24875


What I did for row #2 was that i took the parent function points and multiplied their x values by -3 because as you should of learned in class (-1/3x) (Horizontal stretch) is actually making the x values get bigger and reflecting them through the y-axis.
What I did for row #3 was that I took the points from row #2 and I multiplied their y values by -2 which doubles them ( Vertical stretch) and reflects them through the x-axis.
What I did for row #4 was that I took the points from row #3 and I subtracted 2 from their x values because (x+2) means x and two to the left and subtracted 4 units down.

I hope this helps a bit!

hey!

Yeah, the last function is written correctly. I guess I'm stuck on how to actually apply the transformations to the original points.

The -1/3 is negative one third, I'm not sure how to write it differently than that at this juncture.

Thanks for all your help!

Okay Im done the table, take a look!