## Precalculus (6th Edition) Blitzer

Domain of $f\left( x \right):\left( -\infty ,\infty \right)$ , Range of $f\left( x \right):\left( -\infty ,5 \right]$
The graph is a parabola. Also, since $f\left( x \right)$ is a polynomial, it exists for every value of $x$ on the real axis. Therefore, the domain of $f\left( x \right)=5-{{\left( x+2 \right)}^{2}}$ is $\left( -\infty ,\infty \right)$. And, since, \begin{align} & {{\left( x+2 \right)}^{2}}\ge 0 \\ & -{{\left( x+2 \right)}^{2}}\le 0 \\ & 5-{{\left( x+2 \right)}^{2}}\le 5 \\ & f\left( x \right)\le 5 \\ \end{align} $\Rightarrow f\left( x \right)\in \left( -\infty ,5 \right]$ So, the range of the function is $\left( -\infty ,5 \right]$.