Explanation
Let's analyze the formula of our function:
[tex]f(x)=(-x-1)^2+3.[/tex]
Note that the expression on the right-hand side makes sense for any real number; then, the domain of f consists of all real numbers.
Now, let's analyze the graph of f:
Note that the function takes values ( "vertical values") from 3 up. The value three is included. Then, the range of the f consists of all y such that
[tex]y\ge3.[/tex]
Answer
The domain of f consists of all real numbers.
The range of the f consists of all y such that
[tex]y\ge3.[/tex]
