Question

which table of ordered pairs represents a function?

first table (top left):

x	y
4	-7
4	-5
4	-2
4	1
4	5

second table (top right):

x	y
0	3
1	2
2	3
3	6
4	11

third table (bottom left):

x	y
-3	1
-2	2
1	3
6	4
-2	-1

fourth table (bottom right):

x	y
-2	4
-1	4
0	4
0	-2
1	-2

Explanation:

To determine which table represents a function, we use the definition of a function: each input (x - value) must have exactly one output (y - value).

Step 1: Analyze the first table (top - left)

In the first table, the x - value is 4 for all ordered pairs. So, the input \(x = 4\) is paired with multiple y - values (\(-7,-5,-2,1,5\)). By the definition of a function, this is not a function.

Step 2: Analyze the second table (top - right)

For the x - values \(0,1,2,3,4\), each x - value is paired with exactly one y - value (\(3,2,3,6,11\) respectively). So, this table satisfies the definition of a function.

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

The x - value \(-2\) is paired with two different y - values (\(2\) and \(-1\)). So, this is not a function.

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

The x - value \(0\) is paired with two different y - values (\(4\) and \(-2\)). So, this is not a function.

Answer:

The table with \(x\) values \(0,1,2,3,4\) and corresponding \(y\) values \(3,2,3,6,11\) (the top - right table) represents a function. In terms of the options (assuming the top - right is, say, option B), the answer is: B. The table with \(x\): \(0,1,2,3,4\) and \(y\): \(3,2,3,6,11\)