# How to find corresponding coordinates?

• Sep 21st 2012, 10:42 AM
misiaizeska
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!
• Sep 21st 2012, 02:07 PM
sakonpure6
Re: How to find corresponding coordinates?
Okay,actually there is only one answer for the image.

Here is how to find it:

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

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

$(2(x+5))=2$
$(x+5)=1$
$(x)=-4$

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

$y=-2(f(2))-4$
$y=-2(3)-4$
$y=-6-4$
$y=-10$

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

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
• Oct 2nd 2012, 03:04 PM
misiaizeska
Re: How to find corresponding coordinates?
Thank you so much!