What's the range of y=-2cos (3x) + 3?

Range [-2,2]

Cosine value varies from - 1 to 1, hence - 2cos 3x can vary from + 2 to - 2. The range of the given function, in interval notation, would thus be [-2,2]. In set builder notation it can be expressed as

{y∈R∣-2≤y≤2 }

It most likely might be wrong though so sorry for that.