# How do you use the vertical line test to show #x^2=xy-1# is a function?

This seems like a function, so let's examine the graph:

graph{y=x+1/x [-5, 5, 10, 10]}

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Apply the vertical line test by drawing vertical lines through the graph. If each vertical line intersects the graph at most once, then x^2 = xy - 1 is a function.

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To use the vertical line test to show that (x^2 = xy - 1) is a function, we need to examine whether any vertical line intersects the graph of the equation (x^2 = xy - 1) at more than one point. If every vertical line intersects the graph at most once, then the equation represents a function.

Rearranging the given equation, we get: [ x^2 - xy + 1 = 0 ]

This equation represents a quadratic function in terms of (x). The vertical line test states that if a vertical line intersects the graph of a function at more than one point, then the relation is not a function.

By applying the vertical line test to the graph of the equation (x^2 - xy + 1 = 0), we can observe that every vertical line intersects the graph at most once. Therefore, the equation (x^2 = xy - 1) represents a function.

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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.

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.

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.

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