Answer
There is symmetry only about the y-axis.
See graph
The intercepts: $(-1,0)$, $(1,0)$, $(0,1)$.
Work Step by Step
$$y=1-|x|$$
Testing for symmetry about the x-axis:
$$-y=1-|x|$$ $$y=-1+|x|$$
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:
$$y=1-|-x|$$ $$y=1-|x|$$
Since the resulting equation is the same as the original equation, there is symmetry about the y-axis.
Testing for symmetry about the origin:
$$-y=1-|-x|$$ $$-y=1-|x|$$ $$y=-1+|x|$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the origin.
Rewriting the equation:
$$y=-|x|+1$$
Finding the vertex with $y=a|x-h|+k$, the vertex is $(0,1)$.
At $x=-1$:
$$y=1-|-1|=0$$
At $x=1$:
$$y=1-|-1|=0$$
Thus, two more points on the curve are $(-1,0)$ and $(1,0)$.
Using the points, the graph is as shown below.
The intercepts are for x-intercept is $(-1,0)$ and $(1,0)$ and for y-intercept is $(0,1)$.
