g(x)=3 sin x domain and range

Question

is the domain: {xER}
range {yEr|3< or = y}?

Answer 1

domain is all real x
range is from y = -3 to y = +3

Answer 2

Note in this question and your last one that the range of the sine function is from -1 to +1 (same with cos or with sin (w t + phi) where phi is a constant phase angle)
therefore range of a sin w t or a cos w t is -a to + a

Answer 3

oh yeah, thanks