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A function must be well defined. This means that every element in the domain maps to only one element in the range. In more math terms, let a and b be in the domain of f such that a = b. If f is a function, then if a = b, f(a) = f(b).
A relation does not need to be well defined. An example of this would be y^2 = 4. y = 2 or -2.
An ordered pair that would be part of a relation but not a function would be (x, y^2) vs an ordered pair possible in a function which would be (x^2, y).
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Is the relation a function?
Not every relation is a function. But every function is a relation. Function is just a part of relation.
When does a relation be a function?
A function is a relation whose mapping is a bijection.
How does graphing the order pairs of a relation can help decide if the relation is a function?
If a relation can be called a function, it means that the relation maps every element to one and only one other element. If you have some ordered pairs and see that, for example, 1 maps to 4 (1,4) and 1 also maps to 7 (1,7) , you don't have a function.
A relation is a special type of function?
No. A relation is not a special type of function.
Give an example of a relation that is NOT a function and explain why it is not a function?
y² = x --> y = ±√x Because there are *two* square roots for any positive number (positive and negative) this will not be a function.
Is the relation a function?
Not every relation is a function. But every function is a relation. Function is just a part of relation.
Can you have a function that is not a relation?
No, a function must be a relation although a relation need not be a functions.
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?
Is a function always a relation and a relation always a function?
yes.
When does a relation be a function?
A function is a relation whose mapping is a bijection.
How does graphing the order pairs of a relation can help decide if the relation is a function?
If a relation can be called a function, it means that the relation maps every element to one and only one other element. If you have some ordered pairs and see that, for example, 1 maps to 4 (1,4) and 1 also maps to 7 (1,7) , you don't have a function.
Is all relation a function?
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.
A relation is a special type of function?
No. A relation is not a special type of function.
What makes a relation a function?
A relation is a mapping from one set to another. It is a function if elements of the first set are mapped to only one element from the second set. So, for example, square root is not a function because 9 can be mapped to -3 and 3.
How do you determine if a relation is a function?
A relation is a function if every input has a distinct output.
Give an example of a relation that is NOT a function and explain why it is not a function?
y² = x --> y = ±√x Because there are *two* square roots for any positive number (positive and negative) this will not be a function.
What are function and relation?
A function is an equation that gives a unique answer. A relation does not. Example: y = 3x + 1 is a function. If I give you x, you can determine y. And that y is unique to that x. So if x = 1, you know y = 4. No other of x gives y = 4 as an answer. So y = 3x + 1 is a function. Example: y = 4x2. So if I give you x = 1, y = 4. But y = 4 if I also give you x = -1. So y = 4x2 is not a function, it is a relation.
