1. **State the problem:** We have a function $g$ defined on the set $\{-2, 1, 3, 5\}$ with the rule $g(x) = -2x + 1$. We want to find the values of $g(x)$ for each $x$ in the domain. 2. **Formula used:** The function rule is $g(x) = -2x + 1$. This means for each input $x$, multiply by $-2$ and then add $1$. 3. **Calculate $g(-2)$:** $$g(-2) = -2(-2) + 1 = 4 + 1 = 5$$ 4. **Calculate $g(1)$:** $$g(1) = -2(1) + 1 = -2 + 1 = -1$$ 5. **Calculate $g(3)$:** $$g(3) = -2(3) + 1 = -6 + 1 = -5$$ 6. **Calculate $g(5)$:** $$g(5) = -2(5) + 1 = -10 + 1 = -9$$ 7. **Summary:** The function values are: - $g(-2) = 5$ - $g(1) = -1$ - $g(3) = -5$ - $g(5) = -9$ This shows how the function maps each input to an output by applying the linear rule with a negative slope and y-intercept at 1.