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The first is a little difficult, but we might be able to eliminate some answers

The point ( 1 , -1)  is on the graph

Note that if we substitute 1 into the polynomial, we can add the coefficients and constant of each polynomial and should come up with -1

So...look at the first answer...we add  2 - 3 - 2  + 1  =  -2   so this is not the answer

Look at the third answer....we add  1 - 2 + 3 + 2 - 1  =  -3  so this is not the answer

Now...look at the second  answer...if we put 4 into the function, we get

(4)^4 -2(4)^3 - 3(4)^2 +2(4) + 1  =   256 - 128 - 48 + 8 + 1  =  89

But we should get   329

So......the fourth answer is correct

Here's my best guess for the second one....assuming that x  is the number of years after 1900, the correct function is third one......see the outputs here for this function  [rounded to the nearest integer ]

https://www.wolframalpha.com/input/?i=.139x+%2B+6.57++for+x++%3D+37,+68,95