finding a function from its graph

[godmatrix]

HI, I'm having trouble finding the function of this graph. As you can see the horizontal and vertical asymptotes are given as well as x and y intercepts. Any help would be greatly appreciated.

 

[Steven G]

I am sorry but I do not see any vertical asymptote. Where do you see one? I suspect that the right end of the graph will be coming back down forming a nice cubic graph. Do you really see what the x-intercepts are?

What is the general equation of a cubic?
How many points do you need to find a cubic equation? Can you find that number of points from the graph?
In the end, place state that the cubic only goes from x=-3 to x=3.

 

[HallsofIvy]

Are you assuming that the graph becomes vertical at x= -3 and becomes horizontal at y= 3? That is not obvious from the picture! And while it looks like the y-intercept is y= -1, the best we can say about the x-intercept is that is is between 0 and 1/2. Unless you are told exactly what the graph is for all x, you cannot "get a function from the graph"

 

[Dr.Peterson]

More generally, you can't "find the function" from any graph! Jomo suspects this is part of a cubic, for example; but I've seen enough cubics to know it is not. (It lacks some necessary symmetry.) And even if I saw one that looked really like the cubics I've seen, I could never be sure it is not, say, a 3.1 power of the variable! Functions can vary far more than most people realize.

Please do as we ask, and quote the entire problem verbatim, just as it was given to you. It can't really ask you to "find the function"; we need to know what you were actually told to do.

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