SOLUTION: Hello there, the topic I am having a question for is functions and whether it represents a function. My question is: 1."Determine whether the equation 4x^2+y^2=8 represents a fun

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Question 979163: Hello there, the topic I am having a question for is functions and whether it represents a function.
My question is:
1."Determine whether the equation 4x^2+y^2=8 represents a function".
I know I first need to solve for y^2 and that would equal ______."
2. Note that for any value of x that gives us positive radicand, there are 2 possible values for y. For instance if x =1 then y= positive and negative sqrt(8-4(1))^2 = _______. Since the value of 1 in the domain corresponds to both 2 and ____ in the range, the relation is not a function."
thank you all so much!!!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is NOT a function because it's possible to have x values correspond to more than one y value. It fails the vertical line test. This figure is an ellipse.

If x = 1, then y = +-2. The fact that x = 1 corresponds to y = 2 and y = -2 means we don't have a function. The x value of 1 must correspond to EXACTLY ONE y value only.