Question

for the below, complete the chart by clicking the appropriate answer in each row. determine whether each set of ordered pairs represents a function. (2,3), (3,4), (4,5), (4,6) 20 (2,6), (4,7), (5,8), (6,9) 21 (4,1), (4,2), (4,3), (4,4) 22 function not a function

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value in the ordered pair \((x,y)\)) has exactly one output (y - value). So we need to check for each set of ordered pairs whether any x - value is repeated with different y - values.

Step2: Analyze the first set: \((2,3),(3,4),(4,5),(4,6)\)

Here, the x - value \(4\) is paired with \(5\) and \(6\). Since one input (\(4\)) has more than one output, this set is not a function.

Step3: Analyze the second set: \((3,6),(4,7),(5,8),(6,9)\)

Check each x - value: \(3\) is paired with \(6\), \(4\) with \(7\), \(5\) with \(8\), \(6\) with \(9\). All x - values are unique and each has exactly one y - value. So this set is a function.

Step4: Analyze the third set: \((4,1),(4,2),(4,3),(4,4)\)

The x - value \(4\) is paired with \(1\), \(2\), \(3\), and \(4\). One input (\(4\)) has multiple outputs, so this set is not a function.

Answer:

• For \((2,3),(3,4),(4,5),(4,6)\): Not a Function
• For \((3,6),(4,7),(5,8),(6,9)\): Function
• For \((4,1),(4,2),(4,3),(4,4)\): Not a Function