Is this an even or odd function?

Question

The corrected exercise from my tutor states that the following is an odd function. I am pretty sure this is not true.

$$f: [-1,3] \rightarrow \mathbb{R}: x \mapsto \begin{equation} =\left\{ \begin{array}{@{}ll@{}} x, & \text{if}\ x \in [-1,1) \\ 0, & \text{if}\ x \in [1,3) \end{array}\right. \end{equation} $$

Clearly for $ -1=x \in D$ we have $f(-x)=f(-(-1))=f(1)=0\neq -f(x)=-f(-1)=1$

Thus f is not odd.

Also $f(-x)=f(-(-1))=f(1)=0\neq f(x)=f(-1)=-1$

This f is not even.

Is this assumption correct? The professor stated that f is uneven.

Answer 1

For the reasons given in the question, the function is neither even nor odd.

Answer 2

For a function to be either even or odd, $x$ in the domain has to imply $-x$ in the domain. So the domain has to be a symmetric neighborhood around $0$. Here the domain is $[-1, 3)$ which does not have this symmetry. Therefore, we have to render the function uneven.