Question

does this relation show y as a function of x?

x	y
3	2
3	2
3	4
3	5
3	-6

□ yes
□ no
why?
□ each input value has only one output value assigned to it.
□ more than one y - value is associated with an x - value.
□ each x - value has only 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 input (x - value) has exactly one output (y - value).

Step2: Analyze the Table

In the given table, the x - value is 3 for all rows, and the y - values are 2, 2, 4, 5, - 6. So, the x - value 3 is associated with multiple y - values.

Step3: Determine the Answer for the First Question

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

Step4: Analyze the "Why?" Options

• Option 1: "Each input value has only one output value assigned to it." This is incorrect because 3 (input) has multiple outputs.
• Option 2: "More than one y - value is associated with an x - value." This is correct because x = 3 is associated with y = 2, 2, 4, 5, - 6 (multiple y - values).
• Option 3: "Each x - value has only one y - value paired with it." This is incorrect as we saw x = 3 has multiple y - values.
• Option 4: "Each x - value is associated with only one y - value." This is incorrect for the same reason as option 3.

Answer:

For "Does this relation show y as a function of x?": No
For "Why?": More than one y - value is associated with an x - value.