To determine if the given relationship represents a function, we need to verify if each input [tex]\( x \)[/tex] value is associated with exactly one output [tex]\( y \)[/tex] value. In other words, no [tex]\( x \)[/tex] value should map to more than one [tex]\( y \)[/tex] value.
The given set of pairs [tex]\( (x, y) \)[/tex] is:
[tex]\[ (7, 5), (5, 2), (6, 4), (7, 8), (8, 6) \][/tex]
We will examine the [tex]\( x \)[/tex] values and check their corresponding [tex]\( y \)[/tex] values:
1. The [tex]\( x \)[/tex] value 7 maps to both 5 and 8.
2. The [tex]\( x \)[/tex] value 5 maps to 2.
3. The [tex]\( x \)[/tex] value 6 maps to 4.
4. The [tex]\( x \)[/tex] value 8 maps to 6.
For a relationship to be a function, each [tex]\( x \)[/tex] value must map to exactly one [tex]\( y \)[/tex] value. Here, we see that the [tex]\( x \)[/tex] value 7 maps to two different [tex]\( y \)[/tex] values (5 and 8). This means that the relationship does not satisfy the criterion for a function.
Since at least one [tex]\( x \)[/tex] value is associated with multiple [tex]\( y \)[/tex] values, the given relationship does not represent a function.
Therefore, the correct answer is:
False
