When we talk about domain, we're looking at the x values where the function can exist. The domain is from negative infinity to positive infinity, since there is no x value for which this function doesn't exist. It's a linear function for all but one point, at which it is also defined as y=1.
There are only two kinds of basic functions that don't have infinite domains. "Rational functions" that have variables in their denominators, like 1/x, have vertical asymptotes when the denominator is equal to zero. Also, "radical functions", like square roots, have limited domains because we can't take a square root of a negative number. The domain of y=√x, for example, is 0 to infinity.
If your teacher likes interval notation, you'll write your answer as (-∞,∞), with parentheses on both ends because the graph can never really reach infinity, so those points aren't included. Your teacher may also want something like {-∞<x<∞}. Notation varies.
I hope this helps, and have fun mathing!
