Does this table represent a function? Why or why not?
| Hours of Training | Monthly Pay |
| :---------------- | :---------- |
| 10 | 1220 |
| 20 | 1420 |
| 30 | 1620 |
| 40 | 1820 |
| 50 | 2020 |
| 60 | 2220 |
| 70 | 2420 |
A. Yes, because the [tex]$x$[/tex]-values are positive numbers.
B. Yes, because every [tex]$x$[/tex]-value corresponds to exactly one [tex]$y$[/tex]-value.
C. No, because each [tex]$x$[/tex]-value is different.
D. No, because none of the [tex]$y$[/tex]-values are the same.
Answer (2)
The problem requires determining if a table represents a function.
A function is a relation where each x-value corresponds to exactly one y-value.
The table shows that each x-value (hours of training) has only one corresponding y-value (monthly pay).
Therefore, the table represents a function, and the correct answer is B: Yes, because every x -value corresponds to exactly one y -value.
Explanation
Understanding the Problem The table shows the relationship between hours of training (x-value) and monthly pay (y-value). We need to determine if this table represents a function. A function is a relation where each input (x-value) corresponds to exactly one output (y-value).
Analyzing the Table Let's examine the table:
When the hours of training are 10, the monthly pay is 1220.
When the hours of training are 20, the monthly pay is 1420.
When the hours of training are 30, the monthly pay is 1620.
When the hours of training are 40, the monthly pay is 1820.
When the hours of training are 50, the monthly pay is 2020.
When the hours of training are 60, the monthly pay is 2220.
When the hours of training are 70, the monthly pay is 2420.
Each x-value (hours of training) has only one corresponding y-value (monthly pay).
Evaluating the Answer Choices Now, let's evaluate the given answer choices:
A. Yes, because the x -values are positive numbers. This is not the correct reason. The positivity of x-values doesn't guarantee a function.
B. Yes, because every x -value corresponds to exactly one y -value. This is the correct definition of a function.
C. No, because each x -value is different. The x-values being different doesn't disqualify it from being a function.
D. No, because none of the y -values are the same. The y-values being different doesn't disqualify it from being a function.
Conclusion Therefore, the correct answer is B. The table represents a function because every x -value corresponds to exactly one y -value.
Examples
In real life, functions are used to model relationships between different quantities. For example, the relationship between the number of hours worked and the amount of pay earned can be represented by a function. If each hour worked corresponds to a specific amount of pay, then the relationship is a function. Understanding functions helps us predict and analyze real-world scenarios.
The table represents a function because every x-value (Hours of Training) corresponds to exactly one y-value (Monthly Pay). Each entry in the table has unique x-values leading to unique y-values without any repetition. Therefore, the correct answer is B: Yes, because every x-value corresponds to exactly one y-value.
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