Answer
The domain and range of the function are $\left( -\infty ,\infty \right)$ and $\left[ -4,\infty \right)$ respectively.
Work Step by Step
The graph is a parabola.
Now, since $f\left( x \right)$ is a polynomial, it exists for every value of $x$ on the real axis.
Therefore, the domain of $f\left( x \right)={{\left( x-3 \right)}^{2}}-4$ is $\left( -\infty ,\infty \right)$.
Also since,
$\begin{align}
& {{\left( x-3 \right)}^{2}}\ge 0 \\
& {{\left( x-3 \right)}^{2}}-4\ge -4 \\
& f\left( x \right)\ge -4 \\
& f\left( x \right)\in \left[ -4,\infty \right) \\
\end{align}$
So, the range of the function is $\left[ -4,\infty \right)$.
