Question

does this relation show y as a function of x?

x	y
-3	-3
0	-5
-3	1
1	7
5	-4

yes
no
why?
each x - value has only one y - value paired with it.
each input value has only one output value assigned to it.
at least one x - value has more than one y - value paired with it.
each x - value is associated with only one y - value.

Explanation:

Step1: Recall function definition

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

Step2: Analyze the table

Check the \( x \)-values: \( x = -3 \) appears twice. For \( x = -3 \), the \( y \)-values are \( -3 \) and \( 1 \). So, one \( x \)-value has multiple \( y \)-values.

Step3: Determine the answer for the first part

Since an \( x \)-value (\( -3 \)) has more than one \( y \)-value, the relation is not a function. So the answer to "Does this relation show \( y \) as a function of \( x \)?" is "No".

Step4: Analyze the "Why?" options

• Option 1: False, because \( x = -3 \) has two \( y \)-values.
• Option 2: False, same reason as above.
• Option 3: True, because \( x = -3 \) (an \( x \)-value) has two \( y \)-values (\( -3 \) and \( 1 \)).
• Option 4: False, same as option 1.

Answer:

First question: No
Second question: At least one x - value has more than one y - value paired with it.