Answer
Testing symmetry with respect to the $y$-axis
Work Step by Step
Testing symmetry with respect to $x$-axis:
$$-y=|x|-4$$ $$y=-|x|+4$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to $x$-axis.
Testing symmetry with respect to $y$-axis:
$$y=|-x|-4$$ $$y=|x|-4$$
Since the resulting equation is the same as the original equation, the equation is symmetric with respect to $y$-axis.
Testing symmetry with respect to origin:
$$-y=|-x|-4$$ $$-y=|x|-4$$ $$y=-|x|+4$$
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.
