Domain of function when open circles are included in graph

Question

how would I write the domain of this function? Would I ignore the part of the graph with the open circles like this?
$\{x \ \ / \ -4 \leq x \leq -2 \text{ or } 1 \leq x \leq 4\}$

Answer 1

To determine the domain, you need to figure out which values of $x$ have corresponding values of $y$ (that is, for which $x$ is $f(x)$ defined. In this case, clearly $[-4,-2]$ is in the domain, and also $-1$ is not. The point you are probably asking about is $x=1$. At $x=1$, even though there is an open circle at the point $(1,2)$, the function is defined at $x=1$, with $f(1) = 1$. So the interval $(-1,4]$ is in the domain of $f$.