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.
O The current in the circuit for the lights in a room as a function of time.
O None of these."

Answer 1

□ 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.

Explanation:

Temperature tends to vary continuously over distance and time.

Altitude rarely changes so abruptly we'd have to say it is a discontinuous function. Even a cliff has a (very high) defined slope.

Taxi charges tend to increment according to a rate schedule. That is, for each passing minute or fraction of a mile, the amount due jumps to a new value. We'd have to say those are discontinuous.

The nature of electrical circuits is such that current is never discontinuous. Even when the circuit is disconnected by a switch, the arcing at the switch contacts ensures the current is continuous as it rapidly goes to zero.