1. **Problem statement:** Given the function $p(t) = t + 3$ and the function $p(t) = -2t + 1$, and a function $q(t)$ such that $q(t + 1) = q(t) + 1$, find $q(1)$, $q(2)$, and $q(3)$. 2. **Understanding the problem:** The function $q(t)$ satisfies the functional equation $q(t + 1) = q(t) + 1$. This means that increasing the input by 1 increases the output by 1. This is a property of a linear function with slope 1. 3. **General form of $q(t)$:** Since $q(t + 1) = q(t) + 1$, $q(t)$ can be written as: $$q(t) = t + c$$ where $c$ is a constant. 4. **Finding $c$ using $q(0)$:** We need an initial value to find $c$. Since it is not given, we can express answers in terms of $c$. 5. **Calculate $q(1)$, $q(2)$, and $q(3)$:** $$q(1) = 1 + c$$ $$q(2) = 2 + c$$ $$q(3) = 3 + c$$ 6. **Summary:** Without additional information, $q(t) = t + c$ and the values are $q(1) = 1 + c$, $q(2) = 2 + c$, $q(3) = 3 + c$. If you have more information about $q(t)$, please provide it to find $c$.