Question 317672
<pre><b>
Any number substituted for y will give a defined value for x,
since any number may be squared and multiplied by 4 and an
answer given. So y can be any number.  Therefore the range is
"all real numbers" or 

Range = {{{"("}}}{{{-infinity}}}{{{","}}}{{{infinity}}}{{{")"}}}


{{{x=-4y^2}}}

Solve for y

{{{-4y^2=x}}}
{{{y^2=-x/4}}}
{{{y= "" +- sqrt(-x)/2}}}

An even-root radical such as a square root radical
cannot caontain a negative number in real mathematics.
So what's under the radical must be greater than or equal 0:

So {{{-x >= 0}}} which becomes {{{x<0}}}

So the domain is {{{"("}}}{{{-infinity}}}{{{","}}}{{{0}}}{{{"]"}}}  

To graph, choose x negative or zero so -x will be positive
and be square-root-able, 


  x |  y
 -------
  0 |  0
 -4 | ±1 
-16 | ±2

{{{drawing(400,4000/19,-17,2,-5,5,
graph(400,4000/19,-17,2,-5,5,sqrt(-x)/2),
graph(400,4000/19,-17,2,-5,5,-sqrt(-x)/2))}}}

Edwin</pre>