Question

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

Explanation:

Step1: Recall function definition

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

Step2: Analyze the relation

• The x - value - 7 is paired with 3 (one y - value).
• The x - value 11 is paired with 5 and 8 (two y - values).

Since the x - value 11 has two y - values paired with it, the relation is not a function. Now let's analyze the options:

• Option 1: Says "Yes, because each x - value has only one y - value paired with it." But 11 has two y - values, so this is wrong.
• Option 2: Says "Yes, because the x - value 11 has two y - values pair with it." A function requires each x to have one y, so a yes here is wrong.
• Option 3: Says "No, because the x - value 11 has two y - values pair with it." This matches our analysis.
• Option 4: Says "No, because each x - value has only one y - value paired with it." The reason for no is wrong as the reason given is a property of a function.

Answer:

C. No, because the x - value 11 has two y - values pair with it.