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Question
6.7-3
Not too tricky of a question here, just identify the type of function using the x and y values.
x y
2 5
3 10
4 17
5 26
6 37
7 50
Thanks!

Answer
Construct a difference table.
x  y
2  5
3 10  5
4 17  7  1
5 26  9  1
6 37 11  1
7 50 13  1
In the 1st difference column, 5 is (10-5)/(3-2) = 5/1 = 5; 7 is (17-10)/(4-3) = 7/1 / 7, etc.
In the 2nd diff. column, the 1st 1 is (7-5)/(4-2) = 2/2 = 1; the 2nd is (9-7)/(5-3) = 2/2 = 1.
The 3rd column is not there since all terms have (1-1) in the numerator.

One way to get the result is to note the top of the y, 1st difference, and 2nd difference is
5, 5, 1.  This gives (1(x-3)+5)(x-2) + 5.  Since 5 - 3 = 2, that gives (x+2)(x-2) + 5.
That is the same as x^2 + 1.  Looking back, 2^2 + 1 = 5, 3^2 + 1 = 10, 4^2 + 1 = 17,
5^2 + 1 = 26, 6^2 + 1 = 37, and 7^2 + 1 = 50.

Since that gives the answer, the function is x^1 + 1.  

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