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 $\displaystyle (2,3)$represents $\displaystyle x=2$ and $\displaystyle y=3$ on $\displaystyle y=f(x)$ So when we sub those points in we get $\displaystyle 3=f(2)$.

2- To find the image of point $\displaystyle (3,2)$ of $\displaystyle y=-2(f(2(x+5))-4$ , first you got to realize that $\displaystyle y=f(x)$ is the parent function of $\displaystyle y=-2(f(2(x+5))-4$ 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 $\displaystyle f(2)$ and that would be the image co-ordinates for x value. Your transformed function would look like this $\displaystyle y=-2(f(2))-4$

$\displaystyle (2(x+5))=2$

$\displaystyle (x+5)=1$

$\displaystyle (x)=-4$

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 $\displaystyle f(2)=3 $ we sub in $\displaystyle 3$ for $\displaystyle f(2)$ in the transformed function and then solve for y.

$\displaystyle y=-2(f(2))-4$

$\displaystyle y=-2(3)-4$

$\displaystyle y=-6-4$

$\displaystyle y=-10$

Therefore the image of point (3,2) on the function $\displaystyle f(x)=y$ is (-4,-10) on the function of $\displaystyle y=-2(f(2(x+5))-4$

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?