How to find corresponding coordinates?

The point (2,3) is one the graph of y=f(x). Determine the corresponding coordinates of this point on the graph of y = -2(f(2(x+5))-4.

Not sure how to do this - if anyone could help I would greatly appreciate it.

I know that there are multiple points, and the answers are : (2,3)/(1,3)/(1,6)/(1,-6)/(-4,-6)/(-4,-10). I'm not sure how to find these - thanks in advance!

Re: How to find corresponding coordinates?

Okay,actually there is only one answer for the image.

Here is how to find it:

1- Point represents and on So when we sub those points in we get .

2- To find the image of point of , first you got to realize that is the parent function of which has just been moved around. So for x co-ordinate for the image, we got to find the number for x in the transformed function that would make the transformed function have and that would be the image co-ordinates for x value. Your transformed function would look like this

Therefore when x= -4we get 2. x= -4 is the x-co-ordinate of the new image point.

Now to solve for y point, we do some substitution.

Since we sub in for in the transformed function and then solve for y.

Therefore the image of point (3,2) on the function is (-4,-10) on the function of

Hope this helped if you have more questions just ask :)

EDIT: Another way of solving this problem would be by applying the transformations to (2,3) in the transformed function

Re: How to find corresponding coordinates?