Question

multiple-choice question
which of these is a function?
(-1, 2), (-1, 3), (4, 5)
(3, 2), (3, 4), (3, 5)
(2, 3), (3, 4), (4, 5)
rewatch

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze the first option \(\{(-1, 2), (-1, 3), (4, 5)\}\)

For the x - value \(-1\), we have two different y - values, \(2\) and \(3\). So this relation is not a function.

Step3: Analyze the second option \(\{(3, 2), (3, 4), (3, 5)\}\)

For the x - value \(3\), we have three different y - values, \(2\), \(4\) and \(5\). So this relation is not a function.

Step4: Analyze the third option \(\{(2, 3), (3, 4), (4, 5)\}\)

For the x - values \(2\), \(3\) and \(4\), each x - value has exactly one y - value (\(3\) for \(x = 2\), \(4\) for \(x=3\) and \(5\) for \(x = 4\)). So this relation is a function.

Answer:

\(\{(2, 3), (3, 4), (4, 5)\}\)