Question

Write a rule for the function:

x -2, -1, 0, 1, 2
y 1/3, 1, 3, 9, 27

Answer 1

y = 3^(x + 1).

Explanation:

Here the y values are increasing by a factor 3 and when x = 0 y = 3,

so y = (3)^1 when x = 0 - that is y = (3)^(0 + 1) = 3.

So y = 3^(x + 1) is the rule.

Check: when x = -2, y = 3^(-2+1) = 3 ^-1 = 1/3.

When x = 1, y = 3(1+1) = 3^2 = 9.