If those are the only values, no.
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.
Y = x2
The domain is the set {-3, -2, 0, 3}. Note that because -2 is mapped to -5 as well as 6, this relationship is not a function.
Yes, but is is not a function because 2 gets mapped to two different values (as does -3).
No. If an x-value is repeated but both values have the same image, you can still have a valid function. x values not repeating is not sufficient if there is no image. For example, consider 1/x and the domain as the integers -3, -2, -1, 0, 1, 2, 3. None of the x values repeats but there is no functional relationship because 1/x is not even defined for x = 0.
no
yes
The first number in each pair must be unique.
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.
The right part of the relation needs to be unique - no numbers may be repeated. It's clear that in this case, you would need to remove more than one pair.
1. One to One -function- 2. One to Many -relation- 3. Many to Many -function-
No, it is not a function.
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.
Y = x2
(2, 4)