Question

look at this set of ordered pairs: (7, 11) (16, 19) (1, 19) (6, 19) (-12, 0) 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

Let's list out the x - values of each ordered pair:

• For the pair \((7,11)\), the x - value is \(7\).
• For the pair \((16,19)\), the x - value is \(16\).
• For the pair \((1,19)\), the x - value is \(1\).
• For the pair \((6,19)\), the x - value is \(6\).
• For the pair \((- 12,0)\), the x - value is \(-12\).

Now, we check if any x - value is repeated. The x - values are \(7\), \(16\), \(1\), \(6\), and \(-12\). All of these x - values are unique (no x - value appears more than once). Even though the y - value \(19\) is associated with \(16\), \(1\), and \(6\), the definition of a function only restricts the x - values from having more than one y - value. Since each x - value has only one y - value, this relation is a function.

Answer:

yes