Answer
The range of $y=x^2$ is $[0,\infty)$ while the range of $g(x)=f(x)+k$ is and $[k,\infty)$.
Work Step by Step
Step $1$. The range of $f(x)=x^2$ is $[0,\infty)$
Step $2$. $g(x)=f(x)+k$ can be obtained by shifting $f(x)$ up $k$ units (when $k\ge0$) or down $k$ units (when $k\lt0$).
Step $3$. Thus the range of $g(x)$ becomes $[k,\infty)$
