Question

which of the following are continuous functions? (select all that apply.) the temperature at a specific location as a function of time. the temperature at a specific time as a function of the distance due west from new york city. the altitude above sea level as a function of the distance due west from new york city. the cost of a taxi ride as a function of the distance traveled. the current in the circuit for the lights in a room as a function of time. none of these.

Explanation:

Step1: Recall continuity concept

A continuous function has no sudden jumps, breaks, or holes.

Step2: Analyze temperature - time

The temperature at a specific location as a function of time changes smoothly without sudden jumps, so it is continuous.

Step3: Analyze temperature - distance

The temperature at a specific time as a function of the distance due west from New York City changes smoothly over distance, so it is continuous.

Step4: Analyze altitude - distance

The altitude above sea - level as a function of the distance due west from New York City can change smoothly over distance (ignoring sudden cliffs etc. in a general sense), so it is continuous.

Step5: Analyze taxi - cost

The cost of a taxi ride as a function of the distance traveled has jumps (e.g., when the fare rate changes at certain distance intervals), so it is not continuous.

Step6: Analyze current - time

The current in the circuit for the lights in a room as a function of time has sudden on - off changes (jumps), so it is not continuous.

Answer:

The temperature at a specific location as a function of time.
The temperature at a specific time as a function of the distance due west from New York City.
The altitude above sea level as a function of the distance due west from New York City.