SOLUTION: determine the domain and range and sketch the graph of the relations defined by {{{x=-4y^2}}}

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Question 317672: determine the domain and range and sketch the graph of the relations defined by x=-4y%5E2
Found 2 solutions by texttutoring, Edwin McCravy:
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
This is the inverse of a parabola, so it opens sideways, to the left. Its vertex is at (0,0).

Its Domain is: x<=0 (x is less than or equal to zero)
Its Range is All real numbers

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

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 = %22%28%22-infinity%22%2C%22infinity%22%29%22


x=-4y%5E2

Solve for y

-4y%5E2=x
y%5E2=-x%2F4
y=+%22%22+%2B-+sqrt%28-x%29%2F2

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+%3E=+0 which becomes x%3C0

So the domain is %22%28%22-infinity%22%2C%220%22%5D%22  

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



Edwin