To which family does the function y is equal to open paren x plus 2 close paren raised to the 1 half power plus 3 belong?

The exponent 1/2 means the expression is a square root: y = √(x + 2) + 3. The shifts inside and outside the radical move the graph, but do not change its function family. Therefore, it belongs to the square root family.

AI-written and checked against the verified answer.