circle, compound curve, elipse . . . .
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A curve
depends what graph....
You always use some model (i.e. function) to fit experimental curve. If you do not know the kind of curve (linear, parabola, Gauss, etc.) you can try to fit with different functions and then compare the residual sum of squares and coefficient of determination of those fit functions. I use MagicPlot for curve fitting, you can try to find something in MagicPlot on-line help.
It depends what kind of curve you're talking about. if it's a circle, and the line is tangent to the circle, then one. If it's a circle, and the line is not tangent to the circle, then two. But if it's a goofy shaped curve then it could be any number. But the most likely answer to your question is 2.
A function describes the relationship between two or more variables. A graph is a kind of visual representation of one or more function. A line or curve seen on a graph is called the graph of a function. * * * * * For any point in the domain, a function can map to only ine point in the range or codomain. In simpler terms, it means that (for a two dimensional graph), a vertical line can intersect the graph of the function in at most one point.