Question

Which of these is a continuous function?

a) The distance a train travels as a function of time.
b) The number of children born as a function of years.
c) Option 1 and Option 2 are both continuous functions.
d) None of the above is a continuous function.

Answer 1

Option A). The distance a train travels as a function of time is a continuous function, while the number of children born as a function of years is a discrete function.

Step-by-step explanation:

The question asks which options are examples of continuous functions. A continuous function is one where the values change smoothly without jumps or breaks in the domain.

a) The distance a train travels as a function of time is indeed a continuous function because distance changes continuously as time progresses. There is no point in time where the train travels a certain distance, and then suddenly, without a fractional interim, travels a different distance.

b) The number of children born as a function of years is actually a discrete function because the number of children can only be whole numbers, and there is a clear jump from one integer to the next.

Therefore, the correct answer is: a) The distance a train travels as a function of time.