We need to find the range of the function $g(x) = x^2 + 12$ for the domain $\{-2, -1, 0, 1, 2\}$.

1. Problem Description

We need to find the range of the function $g(x) = x^2 + 12$ for the domain $\{-2, -1, 0, 1, 2\}$.

2. Solution Steps

The range of a function is the set of all possible output values (y-values) we get after plugging in each input value (x-value) from the domain into the function.

Given the function $g(x) = x^2 + 12$ and the domain $\{-2, -1, 0, 1, 2\}$, we will evaluate the function for each value in the domain:

For $x = -2$:

$g(-2) = (-2)^2 + 12 = 4 + 12 = 16$

For $x = -1$:

$g(-1) = (-1)^2 + 12 = 1 + 12 = 13$

For $x = 0$:

$g(0) = (0)^2 + 12 = 0 + 12 = 12$

For $x = 1$:

$g(1) = (1)^2 + 12 = 1 + 12 = 13$

For $x = 2$:

$g(2) = (2)^2 + 12 = 4 + 12 = 16$

The range consists of the set of these output values: $\{16, 13, 12, 13, 16\}$.

Removing duplicates, we have $\{12, 13, 16\}$.

3. Final Answer

$\{12, 13, 16\}$