Respuesta :
We have the equation a)
[tex]\begin{gathered} y^2=8x\text{ } \\ y=\sqrt[]{8x} \end{gathered}[/tex]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:
[tex]\begin{gathered} 0=8x \\ x=0 \end{gathered}[/tex]Intercept in x-axis x=0, we replace in the equation and solve for y:
[tex]\begin{gathered} y^2=8\cdot0 \\ y=0 \end{gathered}[/tex]Only one intercept in the parabola (0,0)
Symmetry:
We check for symmetry about the x-axis, replacing the y for -y:
[tex]\begin{gathered} (-y)^2=8x \\ y^2=8x \end{gathered}[/tex]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:
[tex]\begin{gathered} y^2=8(-x) \\ y^2=-8x \end{gathered}[/tex]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.
