Write a rule for the function:

x - 2, - 1, 0, 1, 2

y 1/147, 1/21, 1/3, 7/3, 49/3

y = 1/3 (7) ^x.

Step-by-step explanation:

Note that the y values increase by a factor 7:

1/21 = 1/147 * 7, 1/3 = 1/21 * 7, and so on.

So the rule is:

y = 1/3 (7) ^x.

Check:

When x = 0, y = 1/3 * (7) ^0 = 1/3

When x = 2, y = 1/3 (7) ^2 = 49/3.

When x = - 2, y = 1/3 (7) ^-2 = 1/3 * 1/7^2 = 1/147.