(a) This is continous because if you are looking at the temperature in a room on a thermometer it does not just suddenly jump to a new temperature. But rather it gradually changes.
The other ones are almost similar.
(d) This is not continous. Because you pay 2 dollars to get in, and ever mile you add .50 cents (for example). Thus, the change from one price to another is not gradual. Rather it skips values.