Removing which ordered pair from the table would make the relation a function of [tex]$x$[/tex]?
| [tex]$x$[/tex] | [tex]$y$[/tex] |
|---|---|
| 1 | 7 |
| 4 | 7 |
| 2 | 2 |
| 4 | 1 |
| 3 | 9 |
A. (1,7)
B. (2,2)
C. (3,9)
D. (4,1)
Answer (2)
The relation is not a function because the x value of 4 is associated with two different y values. Removing the ordered pair ( 4 , 1 ) will make the relation a function because then x = 4 will only be associated with y = 7 . Therefore, the answer is ( 4 , 1 ) .
Explanation
Understanding the Problem We are given a relation in the form of a table of ordered pairs ( x , y ) . A relation is a function if each x value is associated with only one y value. We need to identify which ordered pair, when removed, will make the relation a function.
Identifying the Issue Looking at the table, we see that the x value of 4 is associated with two different y values: 7 and 1. This means that the relation is not a function as it is.
Finding the Culprit To make the relation a function, we need to remove one of the ordered pairs containing x = 4 . The ordered pairs are ( 4 , 7 ) and ( 4 , 1 ) .
Analyzing the Options The options given are ( 1 , 7 ) , ( 2 , 2 ) , ( 3 , 9 ) , and ( 4 , 1 ) . We need to determine which of these options, when removed, will make the relation a function.
Testing Option (4,1) If we remove ( 4 , 1 ) , the remaining ordered pairs are ( 1 , 7 ) , ( 4 , 7 ) , ( 2 , 2 ) , and ( 3 , 9 ) . In this case, x = 4 is only associated with y = 7 , so the relation is a function.
Conclusion Therefore, removing the ordered pair ( 4 , 1 ) will make the relation a function.
Examples
In real life, functions are used to model relationships between different quantities. For example, the amount of money you earn is a function of the number of hours you work. If each hour worked corresponds to only one amount earned, then the relationship is a function. Understanding functions helps us predict and analyze real-world phenomena.
The ordered pair that should be removed to make the relation a function is (4, 1). This is because removing it ensures that the x value of 4 is associated with only one y value, fulfilling the definition of a function.
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