Question

unit d functions test review
the table shows a relation between x and y

x	y
-6	5
-2	2
0	5
1	-1
3	-2

does the relation in the table represent a function?
○ yes, because for each output value, there is exactly one input value.
○ no, because for every input value, there is more than one output value.
○ yes, because each x - value is paired with exactly one y - value.
○ no, because each y - value is paired with exactly one x - value.

Explanation:

To determine if a relation is a function, we use the definition: a function is a relation where each input (x - value) has exactly one output (y - value). Let's check the x - values in the table: - 6, - 2, 0, 1, 3. Each of these x - values is paired with only one y - value.

• The first option is incorrect because the definition of a function is about input to output, not output to input.
• The second option is incorrect as we can see from the table that each x - value has only one y - value.
• The fourth option is incorrect because the fact that a y - value can be paired with one x - value does not determine if it's a function (and also the reasoning for "No" is wrong here).
• The third option is correct as it follows the definition of a function (each x - value has exactly one y - value).

Answer:

C. Yes, because each \( x \)-value is paired with exactly one \( y \)-value.