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I am learning how to graph equations. I think $y=x$ is a line and $y=x^2$ is a parabola. I have a wiggly graph. The question is to find an equation for the graph. It then asks given any graph can you find an equation for it?

I don't think it is the case.

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If you know it's a polynomial you could find its degree, choose that many points, and interpolate a polynomial going through those points. But that doesn't sound like pre-calculus. –  Waleed Khan Mar 14 '13 at 16:47
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There are three issues that come to my mind: 1) What is meant by 'graph' (any mapping $x \mapsto f(x)$, or just any reasonable smooth line)? 2) What is meant by 'equation' (which functions can you use? for any graph you could define its mapping as 'g' and write $y=g(x)$ 3) What is meant by 'find'? (is the trivial solution of 2) ok, or do you have to find it with only a calculator)? –  cubic lettuce Mar 14 '13 at 17:16
    
Evidently, you can do just about anything: wolframalpha.com/input/?i=Rolling+stones+curve –  Mark McClure Mar 14 '13 at 18:03

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If you have graf composed using the inaccurate values use approximation: Least squares method. If you have exact values in graf You can use interpolation method using polynome - for n point use polynome order n.

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