Answer
There is no symmetry about the x-axis, about the y-axis nor the origin.
See graph
The intercepts: $(6,0)$, $(0,6)$
Work Step by Step
$$y=|x-6|$$
Testing for symmetry about the x-axis:
$$-y=|x-6|$$
$$y=-|x-6|$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the x-axis.
Testing for symmetry about the y-axis:
$$y=|-x-6|$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the y-axis.
Testing for symmetry about the origin:
$$-y=|-x-6|$$ $$y=-|-x-6|$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the origin.
Finding the vertex with $y=|x-h|+k$, the vertex is $(6,0)$.
At $x=0$:
$$y=|0-6|=6$$
At $x=9$:
$$y=|9-6|=3$$
Thus, two more points on the curve are $(0,6)$ and $(9,3)$.
Using the points, the graph is as shown below.
The intercepts are for x-intercept is $(6,0)$ and for y-intercept is $(0,6)$.
