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Q: If a vertical line drawn through a graph crosses it only once the relation is a function?

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By doing a vertical line test. If you can draw a vertical line and it only passes through the graph once, its a function. If it passes through twice, it is NOT a function.

the line that crosses through the origin

If the function is a straight line equation that passes through the graph once, then that's a function, anything on a graph is a relation!

If a vertical line passes through the supposed function at only one spot then you have a function.

The vertical line test! Imagine a vertical line going through all points of the graph. As long as the vertical line only touches the graphed line once, it's a function. If it touches more than once, it is not.

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A relation is a function when an x value only has one y value associated with it. An easy way to tell this is to graph the relation, then draw a vertical line through it. If, at any point, it touches the graph twice, the relation isn't a function.

You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).

Horizonatal line test is a test use to determine if a function is one-to-one. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one. A one-to-one function is a function where every element of the range correspons to exactly one element of the domain. Vertical line test is a test used to determine if a function is a function or relation. If you can put a vertical line through graph and it only hits the graph once, then it is a function. If it hits more than once, then it is a relation.

By doing a vertical line test. If you can draw a vertical line and it only passes through the graph once, its a function. If it passes through twice, it is NOT a function.

the line that crosses through the origin

If the function is a straight line equation that passes through the graph once, then that's a function, anything on a graph is a relation!

The "vertical line test" will tell you if it is a function or not. The graph is not a function if it is possible to draw a vertical line through two points.

If a vertical line passes through the supposed function at only one spot then you have a function.

A function is not a function if it passes through the vertical line test more than once, and it is not linear or a quadratic.

Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.

A relation is any set of ordered pairs (x, y), such as {(2, 5), (4, 9), (-3, 7), (2, 0)} or {(2, 3), (5, -2)}. A function is a special type of relation in which each x-value is assigned a unique y-value. So in the two examples given above, the first relation is NOT a function because the x-value of 2 is assigned two different y-values: 5 and 0. The second example above is a relation, since each x-value given (i.e., 2 and 5) is only assigned to one y-value (i.e., 3 and -2, respectively). Two additional examples: {(0, 5), (1, 3), (1, 8), (4, -2)} is NOT a function, because the x-value of 1 is assigned to two different y-values. {(0, 3), (1, 4), (3, -2), (4, 7), (5, 0)} is a function, because there is no x-value that is assigned to more than one y-value. When graphed in the Cartesian plane, you can determine if a relation is a function or not by the "vertical line test", which says that if there is any place where a vertical line can be drawn that will pass through the graph more than once, then that relation is NOT a function. But if every vertical line that can possibly be drawn only passes through the relation at most once, then that relation is a function.

f(x) = x2 This is a function by the vertical line test because a vertical line drawn through this function will only intersect the function at one point