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
