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A relation in which each element of the input is paired with exactly the one element of the output according to a specific rule?
Is called "function".
Differentiate a relation to a function?
A function is a special type of relation. So first let's see what a relation is. A relation is a diagram, equation, or list that defines a specific relationship between groups of elements. Now a function is a relation whose every input corresponds with a single output.
True or false a function is a relation that assigns each input exactly one output?
This is true. Furthermore, functions can be broken down into one-to-one (each input provides a different output), and onto (all of Y is used when f(x) = y).
A relation may assign more than one output value to one of its input values?
True
A relation may not assign more than one output value to one of its input values?
false
What is a mathematical relationship in which each input corresponds to exactly one output?
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'.
In a relation the input is the number of people and the output is the number of phones. Is this relation a function Why or why not?
Yes, this relation is a function because each input (number of people) corresponds to exactly one output (number of phones). In other words, for every specific number of people, there is a unique number of phones associated with that quantity, ensuring that no input has multiple outputs. This satisfies the definition of a 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.
Is every relation a function?
No, not every relation is a function. In order for a relation to be a function, each input value must map to exactly one output value. If any input value maps to multiple output values, the relation is not a function.
A relation with exactly one output for each input?
It's a type of function
Is ordered pairs a relation or function?
An ordered pair can represent either a relation or a function, depending on its properties. A relation is simply a set of ordered pairs, while a function is a specific type of relation where each input (first element of the pair) is associated with exactly one output (second element of the pair). If an ordered pair is part of a set where each input corresponds to only one output, it defines a function. Otherwise, it is just a relation.
What is the relation that assigns exactly one output value to one input value?
It is a bijective function.
If there is a vertical line that intersects the graph of a relation in more than one point then the relation is a functionAsk us anything?
This statement is false. A vertical line intersecting the graph of a relation at more than one point indicates that for at least one input value (x-coordinate), there are multiple output values (y-coordinates). Therefore, the relation does not satisfy the definition of a function, which requires that each input corresponds to exactly one output.
What is the relationship that assigns exactly one output for each input value called?
The relationship that assigns exactly one output for each input value is called a "function." In mathematical terms, for a relation to be classified as a function, every input from the domain must correspond to exactly one output in the codomain. This ensures that there are no ambiguities regarding the output for any given input. Functions are often represented as f(x), where x is the input.
What is a relation with the property that for each input there is exactly one output?
That's a proper function, a conformal mapping, etc.
What test tells if a relation is a function?
To determine if a relation is a function, you can use the "vertical line test." If any vertical line drawn on the graph of the relation intersects the graph at more than one point, then the relation is not a function. Additionally, in a set of ordered pairs, a relation is a function if each input (or x-value) corresponds to exactly one output (or y-value).
