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.'

Answer 1

Answer with Step-by-step explanation:

A continuous function is a function that is defined for all the values in it's domain without any sudden jumps in the values in the domain of the function. All the given situations are analysed below:

1) The temperature at la location as a function of time is continuous function since at any location the temperature is defined for all the time and the temperature cannot suddenly change from say 10 degrees Celsius to 100 degrees Celsius instantly without passing through intermediate values.

2) The temperature at a specific time as a function of the distance due west from New York city is a continuous function as temperature is defined for all the instants of time without any sudden changes as we move between places.

3) The altitude as an function of distance due west from New York is a discontinuous function as there may be sudden changes in the altitude due to changes in topography such as presence of cliff or valley.

4) The cost as a function of function of distance traveled is a discontinuous function since the cost of travel increases integrally in increments of distance and not in a continuous manner.

5) The current in a circuit as function of time is discontinuous function as the current jumps instantly from 0 to a non zero value when we switch on the circuit and same is true when we switch off the circuit it's value decreases instantly to 0.