Explain why each function is continuous or discontinuous. (a) the temperature at a specific location as a function of time (b) the temperature at a specific time as a function of the distance due west from new york city (c) the altitude above sea level as a function of the distance due west from new york city (d) the cost of a taxi ride as a function of the distance traveled (e) the current in the circuit for the lights in a room as a function of time

(a) The temperature at a specific location as a function of time.

This is a continuous function as the temperature cannot increase in an instant like time.

(b) The temperature at a specific time as a function of the distance due west from New York City.

This is a continuous function as the temperature in one location is affected by its neighboring places.

(c) The altitude above sea level as a function of the distance due west from New York City.

The altitude above sea level can be discontinuous at a cliff, or continuous at very deep hole.

(d) The cost of a taxi ride as a function of the distance traveled.

This is a discontinuous function as the cost still raises if you make a stop.

(e) The current in the circuit for the lights in a room as a function of time.

This is a discontinuous function as the function takes the value of 0 when the switch is off and 1 when the switch is on.

The electron traveling speed makes this discontinuous.

the correct answer is the second option

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .