The domain of the function is the entire real number line, except for x=0 where the function is undefined. The function displays unexpected behavior at x=0.

[CODE]:
```python
import math

def f(x):
    if x == 0:
        return None
    else:
        return math.sin(x) / x
```

This code snippet approximates the behavior of the function by explicitly checking for the undefined case at x=0 and using the `math.sin(x)` and `x` functions to calculate the output.