Which of the relations given by the following sets of ordered pairs is a function? (3,-3),(3,-1),(3,1),(3,3),(3,5) (1,2),(2,3),(3,4),(5,6),(2,1) (2,-8),(1,-4),(0,0),(1,4),(2,8) (-2,5),(7,5),(-4,0),(3,0),(1,-6)

## Step 1: Define the criteria for a function<br />### A relation is a function if every input (first element of each ordered pair) corresponds to exactly one output (second element). This means no input value can be repeated with different outputs.<br /><br />## Step 2: Analyze the first set of ordered pairs<br />### The first set is \( \{(3,-3),(3,-1),(3,1),(3,3),(3,5)\} \). Here, the input \( 3 \) is repeated multiple times with different outputs (\(-3, -1, 1, 3, 5\)). Therefore, this set does not define a function.<br /><br />## Step 3: Analyze the second set of ordered pairs<br />### The second set is \( \{(1,2),(2,3),(3,4),(5,6),(2,1)\} \). The input \( 2 \) is repeated with two different outputs (\(3\) and \(1\)). Hence, this set does not define a function.<br /><br />## Step 4: Analyze the third set of ordered pairs<br />### The third set is \( \{(2,-8),(1,-4),(0,0),(1,4),(2,8)\} \). The inputs \( 2 \) and \( 1 \) are repeated with different outputs (\(-8, 8\) for \( 2 \), and \(-4, 4\) for \( 1 \)). Thus, this set does not define a function.<br /><br />## Step 5: Analyze the fourth set of ordered pairs<br />### The fourth set is \( \{(-2,5),(7,5),(-4,0),(3,0),(1,-6)\} \). Each input (\(-2, 7, -4, 3, 1\)) is unique and corresponds to exactly one output (\(5, 5, 0, 0, -6\)). Therefore, this set defines a function.