Answer
Symmetry with respect to the $x$-axis
Work Step by Step
Testing symmetry with respect to $x$-axis:
$$x=(-y)^2-5$$ $$x=y^2-5$$
Since the resulting equation is the same as the original equation, the equation is symmetric with respect to $x$-axis.
Testing symmetry with respect to $y$-axis:
$$-x=y^2-5$$ $$x=-y^2+5$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to $y$-axis.
Testing symmetry with respect to origin:
$$-x=(-y)^2-5$$ $$-x=y^2-5$$ $$x=-y^2+5$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to origin.
The sketch of the graph is as shown.
