True or False: The point $(-3,10)$ is part of the solution region for the inequality $y\ge x^2+2$.

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y>x^2+x$.

A system of inequalities is defined by: $$\{\begin{array}{l}y>x^2\\ y<4\end{array}$$ Which description best fits the feasible region?

Fill in the blank: In the rational inequality $y\le \frac{2x}{x+4}$, even though the inequality is non-strict, the vertical asymptote at $x=-4$ is always drawn as a ________ line.

True or False: For the inequality $y<\frac{1}{x^2+1}$, the entire solution region lies strictly below the horizontal asymptote $y=0$.