What is the domain of a function?

The domain of a function is defined as the set of all first coordinates (or input values) of the ordered pairs that make up the function. In mathematical terms, the domain includes all the values for which the function is defined. Each input is paired with an output in such a way that the function assigns a unique output for each input.

This definition is crucial for understanding how functions operate; knowing the domain allows one to identify which values can be used in the function without running into issues like division by zero or taking the square root of negative numbers, which are situations that could result in undefined outputs.

In contrast, the other choices provide incorrect or irrelevant descriptions regarding the domain. For example, mentioning second coordinates relates to the range of the function, not the domain. Similarly, the collection of all values a function can output refers to the range rather than the input values found in the domain. Lastly, the reference to the graph of all linear relations does not relate to defining what a domain is within the context of a function.