My answers don't exactly jive with those above, but I'm primarily interested in seeing if you've thought about them! My reasons are as follows:
- continuous - same as above
- not a function(!) - So you pick a "transect" due west from NYC. Suppose you intersect a cliff, with an overhang? Do you take your temperature reading from below the cliff or above? The temperatures are not likely to be the same.
- not a function(!) - the "cliff problem" noted above is again the issue.
- discontinuous - same as above - every 1/10th of a mile or so the meter clicks another quarter (or somesuch).
- discontinuous - When the circuit is broken, the current drops instantaneously (for you purists, you might argue that it just drops precipitously, yet continuously!) to zero.
This person might have added something about the endpoints: since the one-sided limits exist, the function is continuous at the endpoints as well. But it's a good effort!