Question

question 4
select all of the following tables which represent y as a function of x.

x	y		x	y		x	y		x	y
-4	0		0	-5		-4	-2		-4	-5
1	2		1	3		3	2		3	1
4	2		1	6		5	2		6	4
8	7		8	9		9	7		8	7
11	12		16	10		3	12		10	13

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Explanation:

To determine if a table represents \( y \) as a function of \( x \), we use the definition of a function: for every input \( x \), there is exactly one output \( y \). In other words, no two \( y \)-values can correspond to the same \( x \)-value.

Step 1: Analyze the first table

\( x \)	\( y \)
1	2
4	2
8	7
11	12

Check for repeated \( x \)-values: All \( x \)-values (-4, 1, 4, 8, 11) are unique. So, each \( x \) has exactly one \( y \). This is a function.

Step 2: Analyze the second table

\( x \)	\( y \)
1	3
1	6
8	9
16	10

Check for repeated \( x \)-values: The \( x \)-value 1 appears twice, with \( y \)-values 3 and 6. Since one \( x \) has two different \( y \)-values, this is not a function.

Step 3: Analyze the third table

\( x \)	\( y \)
3	2
5	2
9	7
3	12

Check for repeated \( x \)-values: The \( x \)-value 3 appears twice, with \( y \)-values 2 and 12. Since one \( x \) has two different \( y \)-values, this is not a function.

Step 4: Analyze the fourth table

\( x \)	\( y \)
3	1
6	4
8	7
10	13

Check for repeated \( x \)-values: All \( x \)-values (-4, 3, 6, 8, 10) are unique. So, each \( x \) has exactly one \( y \). This is a function.

Answer:

The first table (with \( x \)-values -4, 1, 4, 8, 11) and the fourth table (with \( x \)-values -4, 3, 6, 8, 10) represent \( y \) as a function of \( x \). So, the selected tables are the first and the fourth ones (the first checkbox and the fourth checkbox should be marked).