#### Answer

domain $(-\infty,\infty)$; range = $[1,\infty)$

#### Work Step by Step

Domain:
$1+x^{2}$ is defined for all real numbers, so the domain is $(-\infty,\infty)$.
Range:
$x^{2}$ is always greater than or equal to 0, so $x^{2}+1\geq1$. This makes the range $[1,\infty)$