## Precalculus (6th Edition)

The given relation does not represent $y$ as a function of $x$. domain: $(-\infty, +\infty)$ range: $(-\infty, -1] \cup [1, +\infty)$
RECALL: Vertical Line Test If all vertical lines will pass through the graph of a relation in at most one point only, then the relation defines $y$ as a function of $x$. To know if the given graph represents $y$ as a function of $x$, perform the vertical line test. Note that vertical lines $x=3$ will pass through the given graph at two points. This means that the graph fails the vertical line test. Thus, the given relation does not represent $y$ as a function of $x$. The graph covers all x-values so the domain is $(-\infty, +\infty)$. The graph covers y-values that are either greater than or equal to $1$ or less than or equal to $-1$. Thus, the range is $(-\infty, -1] \cup [1, +\infty)$.