How do you use the vertical line test to show #x-y^2=0# is a function?

Answer 1

You can not use the vertical line test to show that #x-y^2 = 0# is a function because it is not a function

Graph for #x-y^2=0#: graph{x-y^2=0 [-5.54, 14.46, -5.08, 4.92]} For all #x>0# a vertical line crosses the line of the equation in two places and therefore the equation does not represent a function.

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Answer 2

Eli Assouline

To use the vertical line test to show that the equation x - y^2 = 0 represents a function, we need to verify that every vertical line intersects the graph of the equation at most once. Rearranging the equation to solve for y, we get y = ±√(x). Both the positive and negative square root functions pass the vertical line test individually, confirming that the equation represents a function. Therefore, x - y^2 = 0 is indeed a function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.