Here's my step-by-step explanation:
The function y = x looks like the attached file. It has no bounds.
It's a continuous function because if you were the poor kid who has to sketch it from the negative infinity to the positive infinity, then you will never have to lift your pencil. There are no gaps or undefined values or spaces that would interrupt that pencil flow.
Therefore, the domain contains all real numbers.
⇔There is no inequality notation.
⇔Interval notation: (-∞,∞)
⇔Set notation: {x : x ∈ R}
