Question

If I were to post a picture of a graph, is there anyway someone could help me figure out its equation?

Answer 1

It would depend on your graph. Some graphs are easier to figure out than others.

Answer 2

This one would be of the more difficult variety, but let me post it for you so you can see what I'm talking about.
http://screencast.com/t/EptnxcG3

Answer 3

The x-axis is just a scale of one. so point a is (1, 197) (2, 203) etc.

Answer 4

Ah, yes, this would be a bit beyond me, but I'll give some sort of input.

From what I can see, there are at least four points where the rate of change changes signs. The end behavior appears to be, if this were a polynomial equation, an odd degree polynomial with a positive leading coefficient. So, because I know that a polynomial of the fifth degree is the lowest of which will match this definition:
- Polynomial of Odd degree
- Derivative of P(x) as a fifth degree polynomial would be a fourth degree polynomial, and we know there are at most four real solutions where P'(x) = 0; thus, at most four lines as horizontal tangents to the graph.

I was thinking the graph would look something like: http://i43.tinypic.com/r2l00p.jpg
From there, however, I'd be stuck since I don't know of a good way to find the regression equation of quintic polynomials. I'm uncertain of whether my inferences would even be correct, in the given situation since I don't know anything else about the graph an I've never done problems like this before. So, I leave this somewhat-of-an answer in hopes that maybe there will be something useful to note in it. :P

Answer 5

Perhaps it may also help to have all of the values of those points, since it's hard to tell their exact location.