Question

Explain why there are restrictions on the domain of a sequence when the sequence is defined as a function.

Answer 1

The domain of any function is the set of x-values.

For a sequence written as a function, the domain is the set of term numbers.  In a sequence, term numbers describe the position of each term in a sequence.  We start a sequence with the first term (1), the second term (2), etc.

When we are counting positions, we do not count half positions or quarter positions; only whole positions are counted.  It would make no sense to say "the first and a half term"; we go from first to second.

This means the domain of the sequence written as a function is restricted to the set of whole numbers.

Answer 2

Answer: The domain of a sequence written as a function is restricted to the set of natural numbers.

Step-by-step explanation:

• Domain of any function is the set of input values of independent variable to a function on which the output values of dependent variable depends.

If a sequence is written as a function, then the domain is the set of natural numbers because the term starts with first term then second then so on.

The number of terms can not be negative or rational.

Here natural numbers represents the position of each term in a sequence. 

This means the domain of the sequence written as a function is restricted to the set of natural numbers.