How can I determine this function? If i know that$$ f(3)-f(-1/2) = 7$$ and $$ f(2)-f(1/2) = 3 $$ and $$f(3/2)-f(-2) =7$$ How can I determine the function? 
 A: $$
f(x) = \left\{
        \begin{array}{ll}
110004 & \quad x = -2 \\
68 & \quad x = -\frac{1}{2} \\
4 & \quad x = \frac{1}{2} \\
110011 & \quad x = \frac{3}{2} \\
7 & \quad x = 2 \\
75 & \quad x = 3 \\
0 & \quad x\neq-2,-\frac{1}{2},\frac{1}{2},\frac{3}{2},2,3
        \end{array}
    \right.
$$
A: One such function would be any linear function of the form 
$$f(x)=2x+c.$$
This comes from observing that the average rate of change (think slope) on each interval is constant,
$$\frac{f(b_i)-f(a_i)}{b_i-a_i}=\frac{7}{3-\left(-\frac{1}{2}\right)}=\frac{3}{2-\left(\frac{1}{2}\right)}=\frac{7}{\frac{3}{2}-(-2)}=2.$$
My guess is that you are being prodded to answer $f(x)=2x+c,\,c\in\mathbb{R}$.
A: Seems to be that f(x) = 2x could satisfy this but I wonder there are a lot more functions that can satisfy this if we work out!!
A: $$f(3) - f(-1/2) = f(3/2)-f(2)$$ this gets you $f(7/2) = 7 $ and you also know that $f(3/2) = 3$. And by substituting $f(3/2) = 3 $ you can also get $f(-2) = -4$I agree with the others that there is information missing and I made some assumptions about the function at hand, but a possible answer is $f(x) = 2x$
