Question

1. consider the relation \\{ (9, 7), (3, 2), (4, 5), (5, 9), (1, 9)\\}. is this relation a function? yes no

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) is associated with exactly one output (y - value). In other words, no two ordered pairs in the relation should have the same first element (x - coordinate) with different second elements (y - coordinates).

Step2: Check the x - values of the ordered pairs

The given relation is \(\{(9, 7), (3, 2), (4, 5), (5, 9), (1, 9)\}\). Let's list out the x - values: \(9\), \(3\), \(4\), \(5\), \(1\). Each of these x - values appears only once. That is, for each x - value, there is exactly one corresponding y - value. Even though the y - values \(9\) is associated with two different x - values (\(5\) and \(1\)), the definition of a function only restricts the x - values from having multiple y - values. So, this relation satisfies the definition of a function.

Answer:

Yes