Final answer:
The provided statement is false since the function f(x) = log3(-x) has a domain of all negative real numbers, not all real numbers, and the concept of horizontal asymptote does not apply to its domain.
Step-by-step explanation:
The statement 'The domain is all real numbers, up to the horizontal asymptote' is false for the function f(x) = log3(-x). The domain of a logarithmic function consists of all positive real numbers when the logarithm is of a positive quantity. In the case of f(x) = log3(-x), the domain would include all negative real numbers because the logarithm requires the argument (-x) to be positive, hence x must be negative.
There is no horizontal asymptote affecting the domain of this function; rather, the vertical line x=0 acts as a vertical asymptote because the log function approaches infinity as the argument approaches zero from the left.