One period of y = 4sin (x) is graphed below. What is the domain of y = 4sin (x) ?

The domain of this sine function is the entire set of real numbers. Since there is no real value of x for which sin (x) becomes undefined, then the entire set of reals is the domain.

(On the other hand, the range would be from - 4 < = y < = 4, since the sine function can only have a value ranging from - 1 to 1, and multiplying 4 expands that from - 4 to 4.)