Let $A = \{x \in R, x \neq 0, -4 \leq x \leq 4\}$ and $f: A \rightarrow R$ be defined by $f(x) = \frac{|x|}{x}$ for $x \in A$. Then, the range of $f$ is
- A$\{1, -1\}$
- B$\{x: 0 \leq x \leq 1\}$
- C$1$
- D$\{x: -4 \leq x \leq 0\}$
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