What is meant by “the domain of a function is (−∞, ∞)”?

Answer 1

that means there is a y for every value of x between −∞ and +∞
for example that would not be true for
y = 7/ (x-1)
because there is no y when x = 1

Answer 2

just for future reference, this domain is good for
all polynomials
all exponentials
all sines and cosines