# How do you decide whether the relation #x = y²# defines a function?

We can graph the relation and do the vertical line test.

Whenever a relation needs to be verified as a function, its graph is created, and the vertical line test is performed.

According to the vertical line test, a relation is considered a function if a vertical line touches the graph only once; if the line touches the graph more than once, it is not a function.

Let us plot this relationship.

sqrtx graph{-10, 10, -5, 5]}

Drawing a vertical line now reveals that the line touches the graph only once overall.

It is therefore a function.

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To determine if the relation (x = y^2) defines a function, you can use the vertical line test. If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. If every vertical line intersects the graph at most once, then the relation is a function. In this case, (x = y^2) does not pass the vertical line test, so it does not define 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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