We have the equation a)
![\begin{gathered} y^2=8x\text{ } \\ y=\sqrt[]{8x} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/i854ub7gobnm6akayx6p6eya9mqrj7b3hv.png)
The domain of a function is the set of all possible inputs for the function. In this case, as a root can not take a negative number, x can not take negative values. The domain would be from 0 to positive infinite.
The intercepts are calculated:
Intercept in y-axis y=0, we replace in the equation and solve for x:

Intercept in x-axis x=0, we replace in the equation and solve for y:

Only one intercept in the parabola (0,0)
Symmetry:
We check for symmetry about the x-axis, replacing the y for -y:

This is identical to the original equation, so we have symmetry about the x-axis.
Now we check for symmetry about the y-axis, replacing in the equation the x for -x:

This is not identical to the original equation since the sign of 8x changes to negative, this means there is no symmetry about the y-axis.