What is the function rule for the given set of x-values: 0, 1, 2, 3 with their respective y-values: 4, 10, 28, 82?

To determine the correct function rule from the given set of x-values (0, 1, 2, 3) and their corresponding y-values (4, 10, 28, 82), we can analyze how the y-values change as the x-values increase.

The function rule provided as 3^(x+1) + 1 suggests an exponential growth model. When substituting the x-values into this function, we can verify whether they yield the expected y-values.

• For x = 0:

( y = 3^{(0+1)} + 1 = 3^1 + 1 = 3 + 1 = 4 ) (matches)

• For x = 1:

( y = 3^{(1+1)} + 1 = 3^2 + 1 = 9 + 1 = 10 ) (matches)

• For x = 2:

( y = 3^{(2+1)} + 1 = 3^3 + 1 = 27 + 1 = 28 ) (matches)

• For x = 3:

( y = 3^{(3+1