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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!

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.

Algebra

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