No it is not. The number 3, in the domain, gets mapped to more than one number in the range.
No, it is not a function.
It is both.
A relation is a set of ordered pairs.A function is a relation such that for each element there is one and only one second element.Example:{(1, 2), (4, 3), (6, 1), (5, 2)}This is a function because every ordered pair has a different first element.Example:{(1, 2), (5, 6), (7, 2), (1, 3)}This is a relation but not a function because when the first element is 1, the second element can be either 2 or 3.
It is both.
If this is the whole of the function, then the domain is {2, 1, -3, -1}. That set can be put in increasing order if you wish but that is not necessary.
If those are the only values, no.
yes
Yes, this relation is a function because each input (the first element in each pair) is associated with exactly one output (the second element in each pair). In this case, all inputs 0, 1, 2, 3, and 4 map to the single output 0, which satisfies the definition of a function. Therefore, it meets the criteria necessary to be classified as a function.
No, it is not 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.
An example of a relation that is not a function is the relation defined by the set of points {(1, 2), (1, 3), (2, 4), (3, 5)}. In this relation, the input value 1 corresponds to two different output values (2 and 3), violating the definition of a function, which states that each input must have exactly one output. Therefore, since one input maps to multiple outputs, this relation is not a function.
1. One to One -function- 2. One to Many -relation- 3. Many to Many -function-
A relation is not a function if it assigns the same input value to multiple output values. In other words, for a relation to be a function, each input must have exactly one output. If an input corresponds to two or more different outputs, the relation fails the vertical line test, indicating that it is not a function. For example, the relation {(1, 2), (1, 3)} is not a function because the input '1' is linked to both '2' and '3'.
Removing one pair is not enough to make it a function. You need to remove one of the pairs starting with 1 as well as a pair starting with 2.
It is both.
A relation is a set of ordered pairs.A function is a relation such that for each element there is one and only one second element.Example:{(1, 2), (4, 3), (6, 1), (5, 2)}This is a function because every ordered pair has a different first element.Example:{(1, 2), (5, 6), (7, 2), (1, 3)}This is a relation but not a function because when the first element is 1, the second element can be either 2 or 3.
It is both.