Answer
Please see the graph.
Work Step by Step
$x^2-y^2 < 1$
$x^2−y^2\lt1 $
This is the graph of a hyperbola, so we have three regions to test for shading. These regions (x-values only) are $(−∞,−1)$, $(−1,1)$, and $(1,∞)$. We use a dotted line since we have a less than sign in the inequality.
We pick the points $(−3,0)$, $(0,0)$, and $(3,0)$.
$(−3,0)$
$x^2−y^2\lt1$
$(−3)^2−0^2\lt1$
$9−0<1$
$9<1$ (false, so we don't shade this area)
$(0,0)$
$x^2−y^2\lt1$
$0^2−0^2\lt1$
$0−0\lt1$
$0\lt1$ (true, so we shade this area)
$(3,0)$
$x^2−y^2\lt1$
$(3)^2−0^2\lt1$
$9−0\lt1$
$9\lt1$ (false, so we don't shade this area)
