Question 587756
For the graph choose the appropriate domain and range. 
2y^2-x^2=8 
divide by 8
y^2/4-x^2/8=1
This is an equation of a hyperbola with vertical transverse axis of the standard form:
(y-k)^2/a^2-(x-h)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.
For given equation:
center:(0,0)
a^2=4
a=2
length of transverse axis=2a=4
..
b^2=8
b=√8
length of conjugate axis=2b=2√8
..
As you can see from the graph below, there are no restrictions on domain and range.
Domain: all real numbers or (-∞,∞)
Range:all real numbers or (-∞,∞)
..
y=±(x^2/2+4)^.5
{{{ graph( 300, 300, -10, 10, -10, 10, (x^2/2+4)^.5,-(x^2/2+4)^.5) }}}