Domain: $(-\infty,\infty)$ See graph.
Work Step by Step
Step 1. The domain requirement is that the denominator can not be zero, which gives $x^2+3\ne0$. Thus the domain can be written as: $(-\infty,\infty)$ Step 2. As $f(-x)=f(x)$, the function is even, and we can not identify any vertical asymptotes. Step 3. As $x\to\pm\infty, y\to4$, we find a horizontal asymptote as $y=4$ Step 4. See graph.