Answer
Domain: $-\infty < x < \infty$
Range: $-\infty < y \leq -1$
Work Step by Step
The equation given is: $f(x) = -2x^2-1$
First, we find the domain. All polynomials are continuous from $(-\infty,\infty)$, so the domain is $-\infty < x < \infty$.
Now, we find the range. This quadratic's equation is $f(x) = ax^2+c$. Since $a$ is negative, the graph is facing downwards, like this: $\bigcap$ Therefore, there is a maximum.
Since there is no horizontal translation, since $b = 0$, the maximum y-value -s $f(0) = -1$.
Thus, the range is from $(-\infty, -1]$. Or, in another form, $-\infty < y \leq -1$