Answer
see graph; domain $(-\infty,\infty)$, range $(-\infty,-2]\cup[2,\infty)$
Work Step by Step
Step 1. From the given equation $\frac{(y)^2}{4}-\frac{(x)^2}{25}=1$, we have $a=2, b=5, c=\sqrt {a^2+b^2}=\sqrt {29}$ centered at $(0,0)$ with a vertical transverse axis.
Step 2. We can find the vertices as $(0,\pm2)$, foci as $(0,\pm\sqrt {29})$, and asymptotes as $y=\frac{a}{b}(x)$ or $y=\pm\frac{2}{5}(x)$
Step 3. We can graph the equation as shown in the figure with domain $(-\infty,\infty)$ and range $(-\infty,-2]\cup[2,\infty)$
