How do you use the vertical line test to show #x^2+y^2=9# is a function?

Answer 1

It is not a function.

For example, the vertical line #x=0# intercepts the curve described by this equation at two points, viz #(0, 3)# and #(0, -3)#. So #y# is not uniquely defined for each value of #x#.

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Answer 2

Jace Anderson

Apply the vertical line test by visually moving a vertical line across the graph of the equation (x^2 + y^2 = 9). If the line intersects the graph at more than one point at any horizontal position, the equation does not represent a function. If the line intersects at only one point for every horizontal position, the equation is 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.