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Determine if the following relationship represents a function.

Choose True or False for the following relationship.
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x \, (\text{input}) & 7 & 5 & 6 & 7 & 8 \\
\hline
y \, (\text{output}) & 5 & 2 & 4 & 8 & 6 \\
\hline
\end{array}
\][/tex]

True

False



Answer :

GinnyAnswer
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

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