Given the function f(x) = 0, since this is a constant function (that is, for any value of x, f(x) = 0, the limit of the function as x->a, where a is any real number, is equal to 0.
More specifically, as a constant function, f(x) maintains the same value for any x. f(1) = f(2) = f(pi) = f(e) = f(-1258567/44) = 0. Further, as a constant function, f(x) is by definition continuous throughout its domain. Note, however, that if one arrives at a constant function via division or multiplication of non-constant functions (for example, (8x)/x, there will still exist a discontinuity where the original denominator was 0).
Graphing the function will further prove this point. On the graph f(x) = 0, the curve is simply the x-axis, which maintains a constant y-value of 0 no matter the x-value.
