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Thread: How to find corresponding coordinates?

  1. #1
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    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!
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  2. #2
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    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
    Last edited by sakonpure6; Sep 21st 2012 at 01:12 PM.
    Thanks from misiaizeska
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    Re: How to find corresponding coordinates?

    Thank you so much!
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