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Relations and functions are very closely related. While all functions are relations, not all relations are functions. That's because functions are a special subset of relations. You can think of a relation as a set containing pairs of related numbers. For example, {(0,0), (1,1), (2,4), (3,9), (4,16)}represents a relation. There are five pairs of numbers. In each pair, the values of the second numbers (known as the range) are dependent upon the values of the first numbers (known as the domain). You can also think of the first number in each pair to be the x value and the second number to be the y value. In other words, y is dependent upon x. So, what makes a relation a function? For a relation to be a function, there must be one and only one y value for each x value. If there are two pairs of numbers that have the same x value but different y values, then the relation is NOT a function. In the above example, the domain is between zero and four, inclusive. Because each x value is unique and has only one corresponding y value, the relation is, in fact, a function. The function is y = x2, which can also be written f(x) = x2.

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A function is always a relation. On the other hand, not all relations are functions. You can consider a function to be a special type of relation (a relation, with additional restrictions or properties).

Always.

Q: When can you say that a relation is a function?

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Not every relation is a function. But every function is a relation. Function is just a part of relation.

A function is a relation whose mapping is a bijection.

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

No. A relation is not a special type of function.

Good question. A relation is simply that; any x-value to create any y-value. A function, however, cannot be defined for multiple values of x. In other words, for a relation to be a function, it must have singular values for all x within its domain.

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Not every relation is a function. But every function is a relation. Function is just a part of relation.

No, a function must be a relation although a relation need not be a functions.

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

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

yes.

A function is a relation whose mapping is a bijection.

Not every relation is a function. A function is type of relation in which every element of its domain maps to only one element in the range. However, every function is a relation.

No. A relation is not a special type of function.

A relation is a function if every input has a distinct output.

Good question. A relation is simply that; any x-value to create any y-value. A function, however, cannot be defined for multiple values of x. In other words, for a relation to be a function, it must have singular values for all x within its domain.

No. A relation is not a special type of function.

relation and function are number that combine with number and neqative number to .