Question

Is this relation a function? If not, explain why.
(0,1) (1,2) (2,3) (3,4) (4,4)

Answer 1

The given relation is a function because each input value (x) is associated with only one output value (y), which fulfills the definition of a function.

Step-by-step explanation:

To determine whether the relation is a function, we need to check if for each input value (x), there is only one output value (y). In other words, every x must be associated with only one y value. So let's examine the given points: (0,1), (1,2), (2,3), (3,4), (4,4).

Observing the first element of each ordered pair, which represents the input or x value, we see that they are all unique: 0, 1, 2, 3, and 4. The second element of each ordered pair, the y value, does not repeat for any x value.

Since no x value is associated with more than one y value, the given relation is indeed a function. This satisfies the definition of a function, where there is a unique correspondence between elements of the domain (x values) and elements of the codomain (y values).

Answer 2

Answer: Yes

Step-by-step explanation:

A relation is considered a function if every input (or domain value) is paired with exactly one output (or range value). In the given relation, each input value is paired with only one output value. For example, the input value 0 is paired with the output value 1, the input value 1 is paired with the output value 2, and so on. Therefore, this relation is a function.