the square root function is defined for:
[tex]D\colon\mleft\lbrace x\in R\colon x\ge0\mright\rbrace[/tex]In this sense, the output values will be greater than or equal to 0, however, since the graph is translated 1 unit down, the range is:
[tex]R\colon\mleft\lbrace x\in R\colon y\ge-1\mright\rbrace[/tex]