Question

are absolute value graphs symmetrical?

Answer 1

yes

Answer 2

About the y-axis yes, but not about the x-axis or any other line.

Answer 3

vertically if \[y=\left| x \right|\]
horizontally if \[x=\left| y \right|\]

Answer 4

and they are not always about the axis for instance if the function is \[y=\left| x-C \right|\] where C is some constant, then it is symmetric about the line x=C