Answer
Please see the graph.
Work Step by Step
$y^2/4 - x^2 \le 1$
This graph is for a hyperbola, and we have three regions to test (for different values of $y$): $(-∞, -2]$, $[-2, 2]$, and $[2, ∞)$. We can use the same $x$ value for the three chosen values of $y$ to test.
Points to use to test: $(0, -3)$, $(0,0)$, $(0,3)$
$(0,-3)$
$y^2/4 - x^2 \le 1$
$(-3)^2/4 - 0^2 \le 1$
$9/4 -0 \le 1$
$9/4 \le 1$ (false)
$(0,0)$
$y^2/4 - x^2 \le 1$
$0^2/4 - 0^2 \le 1$
$0/4 - 0 \le 1$
$0-0 \le 1$
$0 \le 1$ (true, so we shade the region with this point)
$(0,3)$
$y^2/4 - x^2 \le 1$
$(3)^2/4 - 0^2 \le 1$
$9/4 -0 \le 1$
$9/4 \le 1$ (false)