Is there an algorithm which solves this?
 

Suppose the some function F1(x)=A*x^2+B*x+C and another function F2=D*x+E.
Then generate a sequence L1={F1(t),F1(t+1),...,F1(t+n)} and L2={F2(t),F2(t+1),...,F2(t+n)}; where t and n are arbitrary integers. Generate another sequence L3={g,g+1,g+n};where g must be less than absolute value of every value of lists L1 and L2 and less than the absolute value of the derivative of F1 and F2. Now set L1{t} = L1{t} mod L3{g} and L2{t}= L2{t} mod L3{g}. Now use some algorithm that receives either L1 or L2 and tells whether the form of the input function was A*x^2+B*x+C or D*x+E. Here is an example:

F1(x)=10*x^2 and F2(x)=100x+1
L1={250,360,490,640,810} ; L2={501,601,701,801,901}; L3={15,16,17,18,19}
new L1={10,8,14,10,12}; new L2={6,9,4,9,8};

algorithm(L1) returns ("quadratic")
algorithm(L2) returns ("linear")

I searched on google for a while but could not find any leads on how the generating function's form can be determined from the remainder list.