Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a function from $\mathbb{Z}$ to $\mathbb{Z}$ defined by $f(x) = ax + b$ for some integers $a$ and $b$. Determine the values of $a$ and $b$.
- A$a = 2, b = -1$
- B$a = 1, b = 2$
- C$a = -2, b = 1$
- D$a = 2, b = 1$
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