Question

is the relation a function? why.
yes, because the x-value 11 has two y-values pair with it.
yes, because each x-value has only one y-value paired with it.
no, because each x-value has only one y-value paired with it.
no, because the x-value 11 has two y-values pair with it.

Explanation:

Step1: Recall Function Definition

A function is a relation where each \( x \)-value (input) has exactly one \( y \)-value (output).

Step2: Analyze the Relation

• Check \( x = -7 \): Maps to \( y = 3 \) (one \( y \)-value).
• Check \( x = 11 \): Maps to \( y = 5 \) and \( y = 8 \) (two \( y \)-values).

Since \( x = 11 \) has two \( y \)-values, the relation is not a function. The fourth option says "No, because the x - value 11 has two y - values pair with it," which matches.

Answer:

No, because the x - value 11 has two y - values pair with it. (The fourth option in the choices)