# How to find corresponding coordinates?

• Sep 21st 2012, 09:42 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, 01:07 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 \$\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
• Oct 2nd 2012, 02:04 PM
misiaizeska
Re: How to find corresponding coordinates?
Thank you so much!