Determine whether the relation is a function. {(5, 9), (4, 8), (-7, 4), (0, 4), (2, 4), (3, 9), (-3, 8)}

Solution:

A relation R from a non-empty set B is a subset of the cartesian product A × B.

The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.

Given, the relation is {(5, 9), (4, 8), (-7, 4), (0, 4), (2, 4), (3, 9), (-3, 8)}

We have to determine whether the relation is a function or not.

To check whether the given relation is a function or not,

We have to check if any of the x-coordinates in any of the ordered pairs are equal.

If there are ordered pairs such that the x-coordinates are equal but the y-coordinates are not equal, the the relation is not a function.

From the relation,

x-coordinates are {5, 4, -7, 0, 2, 3, -3}

y-coordinates are {9, 8, 4, 4, 4, 9, 8}

We see that each x-value is paired with exactly one y-value.

We see that x values are not repeating.

Therefore, the given relation is a function.

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Determine whether the relation is a function. {(5, 9), (4, 8), (-7, 4), (0, 4), (2, 4), (3, 9), (-3, 8)}

Summary:

The relation {(5, 9), (4, 8), (-7, 4), (0, 4), (2, 4), (3, 9), (-3, 8)} is a function.