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What else can I help you with?
Which ordered pair could you remove from the relation 1 0 1 3 2 2 2 3 3 1 so that it becomes 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.
What is the function for this function table x -3 -2 0 1 2 y 9 4 0 1 4?
Y = x2
What is the domain of this relation (-3 0) (-2 -5) (-2 6) (3 7) (0 -17)?
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.
Is this a relation (-3 2) (2 -4) (2 6) (-3 -5) (0 -3)?
Yes, but is is not a function because 2 gets mapped to two different values (as does -3).
Is a function a relation if and only the x-values do not repeat in a given set?
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.
Is this relation a function{(0, 0), (0, 1), (0, 2), (0, 4), (0, 5)}?
no
Is this relation a function{(0, 0), (1, 0), (2, 0), (3, 0), (4, 0)}?
yes
Which ordered pair could you remove from the relation 2 1 1 1 1 0 0 1 1 0 so that it becomes a function?
The first number in each pair must be unique.
Does (4-2)(1-1)(00)(42) represent a function?
The expression (4-2)(1-1)(00)(42) does not represent a function in a mathematical sense. A function is defined as a relation where each input corresponds to exactly one output. In this case, the expression simplifies to 2(0)(0)(42), which equals 0, but it does not define a relationship between inputs and outputs in the way that a function does. Therefore, it is not a function.
How can you tell if a relation of a graph has 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.
Which ordered pair could you remove from the relation -2-1 -11 -10 01 10 so that it becomes a function?
To determine which ordered pair to remove from the relation ((-2, -1), (-1, -10), (0, 1), (1, 0)), we need to ensure that each input (first element) has a unique output (second element). In this case, the relation does not have any repeated first elements, so it is already a function. Therefore, no ordered pair needs to be removed to maintain the function definition.
Which ordered pair could you remove from the relation (2 1) (1 1) (1 0) (0 1) (1 0) so that it becomes 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.
What are the kinds of relation in mathematics?
1. One to One -function- 2. One to Many -relation- 3. Many to Many -function-
What is an example of a relation that is not 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.
how is a relation not a 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'.
Which ordered pair could you remove from the relation 1 0 1 3 2 2 2 3 3 1 so that it becomes 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.
Is this relation afunction (-32)(2-4)(26)(-3-5)(0 3)?
No, it is not a function.
