# Thread: Write the closest equation of the function that this graph represents--help please

1. ## Write the closest equation of the function that this graph represents--help please

I know how to graph rational functions, but I'm having trouble writing a function given the graph. Can someone help me out with this?

<a href="http://s1015.photobucket.com/albums/af279/tom555_photo/?action=view&amp;current=IMG_1886.jpg" target="_blank"><img src="http://i1015.photobucket.com/albums/af279/tom555_photo/IMG_1886.jpg" border="0" alt="Photobucket"></a>

2. ## Re: Write the closest equation of the function that this graph represents--help pleas

$\displaystyle y = \frac{ax+b}{cx+d}$

vertical asymptote at $\displaystyle x = 4$ ... $\displaystyle 4c+d = 0$

horizontal asymptote at $\displaystyle y = 2$ ... $\displaystyle \frac{a}{c} = 2$

$\displaystyle y(0) = 1$ ... $\displaystyle \frac{b}{d} = 1$

$\displaystyle y(2) = 0$ ... $\displaystyle 2a+b = 0$

see what you can do with it now.

3. ## Re: Write the closest equation of the function that this graph represents--help pleas

Thanks for the reply, but I'm not exactly sure what all that means above (I'm in an honors level algebra 2 course if that helps). I know where the asymptotes and the intercepts are, but how do I use them to figure out the equation? I know that in the denominator there has to be (x-4) and the equation has to look something like 2x/x to satisfy to horizontal asymptote.

- also that to find the y-intercept I plug in zero for x, and to find the x-intercept I set the numerator equal to zero

4. ## Re: Write the closest equation of the function that this graph represents--help pleas

Originally Posted by mathguy5
Thanks for the reply, but I'm not exactly sure what all that means above (I'm in an honors level algebra 2 course if that helps). I know where the asymptotes and the intercepts are, but how do I use them to figure out the equation?
the equation is the general form for a rational equation where a, b, c, and d are all constants ... I've given you some constraints for the values of the constants based upon information from the graph.

5. ## Re: Write the closest equation of the function that this graph represents--help pleas

Sorry, I'm still a little lost. What do I do besides c=1? I'm not familiar with the "general form," I suppose. I know how to graph a given rational function, but I'm confused as to how to produce the function given a graph.

6. ## Re: Write the closest equation of the function that this graph represents--help pleas

Is it f(x)= 2x(x-2)/x(x-4)?

8. ## Re: Write the closest equation of the function that this graph represents--help pleas

Originally Posted by mathguy5
Is it f(x)= 2x(x-2)/x(x-4)?
f(x)= 2(x-2)/(x-4)

the additional x in the numerator and denominator creates a point discontinuity at x = 0 which the graph does not have.

9. ## Re: Write the closest equation of the function that this graph represents--help pleas

Thanks to all who responded and PM'd me