Q: find function of a graph if we know x and y points I need to know how to find the function of a given values of a graph 
the known points are $$ (x,y)= 
(3.6,40) \quad \text{and} \quad 
(4.7,20) \quad\text{and}\quad
(7.3,5)
$$.Any reference how to solve this ? 
Thanks ! 

A: This is a complete guess with no real reasoning behind it, but I'm going to assume a relation like this:
$$
x(y) = \frac{1}{a+by} = \frac{1}{g(y)}
$$
with some constants $a$ and $b$. If I calculate the values of $g(y)$, I get the following pairs of points:
$$
\left(\frac{1}{x}, y \right) = (40, \frac{1}{3.6}); (20, \frac{1}{3.6}) \qquad \text{and} \qquad (5, \frac{1}{7.3}) 
$$
With linear regression I get approximately
$$
g(y) \approx 0.123 + \left(3.98\cdot 10^{-3}  \right)y
$$
and therefore the simplest way to approximate the function $x(y)$ would be
$$
x(y) \approx \frac{1}{0.123 + \left(3.98\cdot 10^{-3}  \right)y}
$$
This results in $x(5) \approx 7.0$, $x(20)\approx 4.94$ and $x(40) \approx 3.54$. It's not perfect, but it's an approximation. I hope this helps.
