The domain of this function is all real numbers except 0, as stated by the inequality x =/= 0.
Yes, the function is continuous on the entire real number line (R), including the point x = 0. This is because the limit of f(x) as x approaches 0 from both the left and right sides is equal to 0, therefore the function is continuous at x = 0.
The range of this function is all real numbers, as the sine function has a range of [-1, 1] and multiplying by x will result in a range of [-x, x].
No, there are no points of discontinuity in this function as it is continuous on the entire real number line.
As x approaches infinity, the function will oscillate between -x and x, getting closer and closer to 0 but never reaching it. This is because the sine function oscillates between -1 and 1 as the input gets larger, and multiplying by x will result in the oscillations getting larger as well.