Let $Z$ be the set of integers. The function $f : Z \rightarrow Z$ is defined as
$$f ( x ) = \begin{cases} x - 1 , & \text{if } x < 0 \\ x + 1 , & \text{if } x \geq 0 \end{cases}$$
Accordingly,
I. f is one-to-one.\\
II. f is onto.\\
III. The range of f is $Z \backslash \{ 0 \}$.
Which of these statements are true?
A) Only I\\
B) Only II\\
C) Only III\\
D) I and II\\
E) I and III