Question

which of these relations are functions? select all that apply.

Explanation:

To determine if a relation is a function, we use the definition: a relation is a function if each input (x - value) has exactly one output (y - value).

Step 1: Analyze the first table (red)

• The x - values are 20, 20, - 8, 10, 17, 17.
• The x - value 20 is paired with - 12 and - 13. The x - value 17 is paired with 12 and 13. Since an x - value has more than one y - value, this relation is not a function.

Step 2: Analyze the second table (orange)

• The x - values are 0, 11, 9, 9, - 13, 2.
• The x - value 9 is paired with - 16 and 20. Since an x - value has more than one y - value, this relation is not a function.

Step 3: Analyze the third table (green - left)

• The x - values are 12, 0, 6, 15, 4, 8.
• Each x - value (12, 0, 6, 15, 4, 8) is paired with exactly one y - value. So this relation is a function.

Step 4: Analyze the fourth table (green - right)

• The x - values are 17, 3, 16, 6, - 18, 15.
• Each x - value (17, 3, 16, 6, - 18, 15) is paired with exactly one y - value. So this relation is a function.

Answer:

The third table (with x - values 12, 0, 6, 15, 4, 8) and the fourth table (with x - values 17, 3, 16, 6, - 18, 15) are functions. In terms of the tables in the image, the third (green - left) and fourth (green - right) tables represent functions.