Answer
There is no symmetry about the x-axis, about the y-axis nor the origin.
See graph
The intercepts are for x-intercept is $(1,0)$ and for y-intercept is $(0,1)$.
Work Step by Step
$$y=\sqrt{1-x}$$
Testing for symmetry about the x-axis:
$$-y=\sqrt{1-x}$$ $$y=-\sqrt{1-x}$$
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:
$$y=\sqrt{1-(-x)}$$ $$y=\sqrt{1+x}$$
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:
$$-y=\sqrt{1-(-x)}$$ $$-y=\sqrt{1+x}$$ $$y=-\sqrt{1+x}$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the origin.
Finding the domain:
$$1-x\geq0$$ $$-x\geq-1$$ $$x\leq1$$
At $x=1$:
$$y=\sqrt{1-1}=0$$
At $x=0$:
$$y=\sqrt{1-0}=1$$
At $x=-3$:
$$y=\sqrt{1-(-3)}=2$$
Thus, three points on the curve are $(1,0)$, $(0,1)$ and $(-3,2)$.
Using the points, the graph is as shown below.
The intercepts are for x-intercept is $(1,0)$ and for y-intercept is $(0,1)$.
