The domain of a function refers to the set of all possible input values (usually represented as ‘x’) that the function can accept. In the case of a sequence of numbers like 3, 2, 6, 1, 1, 4, 5, 9, 4, 0, we need to clarify how this sequence is expressed as a function.
Assuming this sequence represents specific outputs of a function for distinct input values, we can conceptualize the domain based on the positions of these outputs. Here’s how:
- The position in the sequence can represent the input values: for instance, the first number corresponds to x = 1 yielding output 3, the second number corresponds to x = 2 yielding output 2, and so forth.
- Therefore, we could construct the function such that for input values: x = 1 maps to 3, x = 2 maps to 2, x = 3 maps to 6, and so on.
This means the domain consists of the set of all input values that correspond to these outputs. For the given sequence, we can deduce that the domain includes the integer values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Therefore, the domain is:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
In conclusion, understanding the domain helps us identify what input values are valid for our function. It’s essential to analyze the context in which a series of numbers is provided to ascertain its domain accurately.