Answer
There is no symmetry about the x-axis, y-axis nor the origin.
See graph
The intercept: $(3,0)$
Work Step by Step
$$y=\sqrt{x-3}$$
Testing for symmetry about the x-axis:
$$-y=\sqrt{x-3}$$ $$y=-\sqrt{x-3}$$
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:
$$y=\sqrt{-x-1}$$
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:
$$-y=\sqrt{-x-1}$$ $$y=-\sqrt{-x-1}$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the origin.
Finding the domain:
$$x-3\geq0$$ $$x\geq3$$
At $x=3$:
$$y=\sqrt{3-3}=0$$
At $x=4$:
$$y=\sqrt{4-3}=1$$
At $x=7$:
$$y=\sqrt{7-3}=2$$
Thus, three points on the curve are $(3,0)$, $(4,1)$ and $(2,7)$.
Finding x-intercept where $y=0$:
$$0=\sqrt{0-1}$$ $$x^3=1$$ $$x=1$$
Thus, a point is at $(1,0)$.
Finding y-intercept where $x=0$:
$$y=0^3-1$$ $$y=-1$$
Thus, another point is at $(0,-1)$.
At $x=-1$:
$$y=(-1)^3-1=-2$$
Thus, another point is $(-1,-2)$
Using the points, the graph is as shown below.
The intercept is only x-intercept which is $(3,0)$.
