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Which of these tables represents a function?
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] & [tex]$x$[/tex] & [tex]$y$[/tex] & [tex]$x$[/tex] & [tex]$y$[/tex] & [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline-1 & 15 & 0 & 4 & 4 & 0 & 6 & -2 \\
\hline-2 & 6 & 6 & 15 & -1 & -2 & 4 & 0 \\
\hline 0 & 15 & 0 & 6 & 6 & -2 & 15 & -1 \\
\hline 4 & 6 & -2 & -1 & 6 & 15 & 4 & 3 \\
\hline
\end{tabular}

A. W
B. X
C. Y
D. Z

Sagot :

GinnyAnswer
To determine which table represents a function, we need to verify that each input [tex]\( x \)[/tex] is associated with exactly one output [tex]\( y \)[/tex]. In other words, there should be no repeated [tex]\( x \)[/tex] values with different [tex]\( y \)[/tex] values.

Let's analyze each column of the table:

- Column W:
- Row 1: [tex]\( (-1, 15) \)[/tex]
- Row 2: [tex]\( (-2, 6) \)[/tex]
- Row 3: [tex]\( (0, 15) \)[/tex]
- Row 4: [tex]\( (4, 6) \)[/tex]

There are no repeated [tex]\( x \)[/tex] values; each [tex]\( x \)[/tex] is matched with exactly one [tex]\( y \)[/tex].

- Column X:
- Row 1: [tex]\( (0, 4) \)[/tex]
- Row 2: [tex]\( (6, 15) \)[/tex]
- Row 3: [tex]\( (0, 6) \)[/tex]
- Row 4: [tex]\( (-2, -1) \)[/tex]

Here, the [tex]\( x \)[/tex] value 0 appears twice with different [tex]\( y \)[/tex] values (first as [tex]\( (0, 4) \)[/tex] and then as [tex]\( (0, 6) \)[/tex]). This means it does not represent a function.

- Column Y:
- Row 1: [tex]\( (4, 0) \)[/tex]
- Row 2: [tex]\( (-1, -2) \)[/tex]
- Row 3: [tex]\( (6, -2) \)[/tex]
- Row 4: [tex]\( (6, 15) \)[/tex]

Here, the [tex]\( x \)[/tex] value 6 appears twice with different [tex]\( y \)[/tex] values (first as [tex]\( (6, -2) \)[/tex] and then as [tex]\( (6, 15) \)[/tex]). This means it does not represent a function.

- Column Z:
- Row 1: [tex]\( (6, -2) \)[/tex]
- Row 2: [tex]\( (4, 0) \)[/tex]
- Row 3: [tex]\( (15, -1) \)[/tex]
- Row 4: [tex]\( (4, 3) \)[/tex]

Here, the [tex]\( x \)[/tex] value 4 appears twice with different [tex]\( y \)[/tex] values (first as [tex]\( (4, 0) \)[/tex] and then as [tex]\( (4, 3) \)[/tex]). This means it does not represent a function.

Based on this analysis, the correct answer is:

A. W
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