Answer
The Domain of the function is $\left( -\infty ,\infty \right)$ and the Range is $\left( -\infty ,-4 \right]$
Work Step by Step
We have to find the range of the function; we use the vertex of the parabola, which is $\left( -3,-4 \right)$. Since the parabola open upwards, the maximum value of the function is given by the y-coordinate of the vertex. Thus, the maximum value is $-4$. The minimum value of the function would be $-\infty $. Thus, the range of the function is $\left( -\infty ,-4 \right]$.
For the domain, one can see the values of the function at which the function is defined. The function is defined at all real values. Thus, the domain of the function is $\left( -\infty ,\infty \right)$.
Thus, the range of the function is $\left( -\infty ,-4 \right]$ and its domain is $\left( -\infty ,\infty \right)$.
