Question

complete the table to create a relation that is not a function.

x	y
-3	-10
0
	4
7

Explanation:

Step1: Recall function definition

A relation is not a function if at least one input (x - value) has more than one output (y - value). So we need to repeat an x - value with a different y - value, or have a new x - value that's same as an existing one with different y. Let's use an existing x - value. The existing x - values are - 3, 0, 7. Let's choose x=-3 (already has y = - 10) and give it a new y - value, or use x = 0, or x = 7. Alternatively, for the empty x (the third row), we can set it to an existing x. Let's set the empty x (third row) to - 3 (existing x with y=-10), and set its y to something else, say 5. Wait, no, the third row has y = 4, so x in third row: let's set x=-3 (same as first row's x). So first row: x=-3, y=-10; third row: x=-3, y = 4. Then for the other empty y's: let's fill 0's y as, say, 2, and 7's y as 8. But the key is to have a repeated x. So let's fill the third row's x as - 3 (so x=-3 appears twice, with y=-10 and y = 4), 0's y as 5, 7's y as 9. Wait, the problem is to complete the table. Let's structure:

First, the table has rows:

1. x=-3, y=-10

1. x = 0, y=?

1. x=?, y = 4

1. x=7, y=?

To make it not a function, we need a repeated x. So let's set the x in row 3 to - 3 (so x=-3 has y=-10 and y = 4). Then row 2: x = 0, y=5 (any number), row 4: x=7, y=8 (any number). So filling:

Row 2 (x=0, y): let's pick y = 3

Row 3 (x): - 3

Row 4 (x=7, y): 6

So the table becomes:

x | y

-3 | -10

0 | 3

-3 | 4

7 | 6

Now, x=-3 has two y - values (-10 and 4), so it's not a function.

Step2: Fill the values

• For x = 0 (second row), choose any y, say y = 5 (or any number, it doesn't matter as long as x is unique here, but the key is the repeated x). Wait, no, the repeated x is the key. So the critical part is the third row's x: set it to - 3 (existing x). Then the other y's can be any values. Let's formalize:

• Second row (x = 0, y): let's put y = 2

• Third row (x): put x=-3 (so x=-3, y = 4)

• Fourth row (x = 7, y): put y = 3

Now, check: x=-3 has y=-10 and y = 4 (two outputs for same input), so not a function.

So the filled table would have:

x | y

-3 | -10

0 | 2

-3 | 4

7 | 3

This works because x=-3 is repeated with different y - values.

Answer:

(One possible completion: )

• For \( x = 0 \), \( y = 2 \) (any value is fine, but the key is the repeated \( x \))

• For the \( x \) in the third row (with \( y = 4 \)), \( x=-3 \) (repeats \( x=-3 \) from the first row)

• For \( x = 7 \), \( y = 3 \) (any value is fine)

(So the table is completed with \( x = 0, y = 2 \); \( x=-3, y = 4 \); \( x = 7, y = 3 \) (or other values, as long as \( x=-3 \) is repeated))

(Note: The specific numbers for \( y \) (except the repeated \( x \) part) can vary, but the key is a repeated \( x \)-value with different \( y \)-values.)