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.