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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.

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Q: How can you tell if a relation of a graph has a function?
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Related questions

When is a relation considered to be function?

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.


How do you determine if a relation represents a function?

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!


Which of these data sets represents a function?

Does the graph above show a relation, a function, both a relation and a function, or neither a relation nor a function?


When can you say that the graph is function or mere relation?

If a vertical line intersects the graph at more than one point then it is not a function.


If no vertical line intersects the graph of a relation in more than one point then the relation is a function?

True.


How can you tell if a graph is a sine function or a cosine function?

sine graph will be formed at origine of graph and cosine graph is find on y-axise


When is a relation also a function?

A relation is also a function if each member of the domain (or x-coordinate) is paired with only one member of the range (or y-coordinate). If the relation is a set of ordered pairs that consists of real numbers a graph can be created to visualize the relation. If a vertical line can be drawn and only crosses or intersects the graph at one point then the relation is also a function.


Without using a graph how can you tell if an equation is a function or relation?

Verticle line test man. If it intersects two points it is its not a function. if it hits one point it is a function. and im currently looking up to see how it is a equation...


The output of a function or relation The set of y-values that a graph is defined on?

Range


How can you tell if a graph sHow is a function?

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.


How do you draw a graph of a relation that is not a function?

A graph that is not a function, fails the vertical line test. You can draw it by connected all ordered pair of points in a rectangular coordinate system.


How does you know that relation is a function?

One way is to try the vertical line test on a graph!