Question

does this table represent a function? why or why not?
hours of training monthly pay
10 1100
20 1200
30 1300
40 1400
50 1500
60 1600
70 1700
a. no, because each x - value is different.
b. yes, because the y - values are positive numbers.
c. no, because none of the y - values are the same.
d. yes, because every x - value corresponds to exactly one y - value.

Explanation:

To determine if a table represents a function, we use the definition of a function: a relation where each input (x - value) has exactly one output (y - value). In the given table, the "Hours of Training" (x - values: 10, 20, 30, 40, 50, 60, 70) are all unique, and each x - value is paired with exactly one "Monthly Pay" (y - value).

• Option A is incorrect because different x - values do not prevent a relation from being a function; in fact, having unique x - values helps.
• Option B is incorrect because the sign of y - values (positive here) is not a criterion for a relation to be a function.
• Option C is incorrect as the fact that y - values are different is not a reason for a relation to not be a function (and also, the reasoning is wrong as the relation here is a function).
• Option D is correct as it follows the definition of a function: every x - value (hours of training) corresponds to exactly one y - value (monthly pay).

Answer:

D. Yes, because every x - value corresponds to exactly one y - value.