Question

look at this set of ordered pairs: (4, 12) (-6, 11) (0, 11) (-16, 12) 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) has exactly one output (y - value). In other words, no two ordered pairs in the relation can have the same x - value with different y - values.

Step2: Check the x - values of the ordered pairs

The ordered pairs are \((4,12)\), \((- 6,11)\), \((0,11)\), \((-16,12)\).

• The x - value \(4\) is paired with \(12\).
• The x - value \(-6\) is paired with \(11\).
• The x - value \(0\) is paired with \(11\).
• The x - value \(-16\) is paired with \(12\).

We can see that each x - value (\(4\), \(-6\), \(0\), \(-16\)) is paired with only one y - value. Even though \(11\) is paired with both \(-6\) and \(0\), and \(12\) is paired with both \(4\) and \(-16\), the definition of a function only restricts that one x - value cannot be paired with multiple y - values. There is no restriction on multiple x - values being paired with the same y - value.

Answer:

yes