If $f(x)$ if a function whose domain is $(-\infty,\infty)$ and whose range is $[-11,3]$, and $g(x) = f(x)+1,$ then what is the range of $g(x)$? Express your answer in interval notation.

Answer 1

Since every output of $f(x)$ is increased by $1$, $g(x)$ obtains every value that $f(x)$ does plus $1$. Since the range of $f(x)$ is $[-11,3]$, the range of $g(x)$ is $\boxed{[-10,4]}$.