How do you find the rule for a function table when the left column is x equals 2 3 4 5 and the right column is 2 5 8 11?

Answer 1

The right column changes by the same amount for each change of one in x.

So Ux is linear. That is, Ux = a + bx

That "same amount" is 3 so b = 3. That gives Ux = a + 3x

There are now two ways to find the value of a.

You can either take any row of the function table and solve the equation. Suppose you take row 3 - which is 4 and 8.

8 = a + 3*4 = a + 12

and that gives a = -4

OR

Take the sequence back two steps to what it would have been when x = 0. The sequence increases by 3 as you move up the xs. So it decreases by 3 for each step back. Then starting from x = 2 and y = 2 and moving back one step gives x = 1 and y = -1. A second step gives x = 0 and y = -4 (as before).

So, the final answer is Ux = -4 + 3x

Answer 2

45