Does this table represent a function? Why or why not?
A. Yes, because there is the same number of $x$-values as $y$-values.
B. No, because one $x$-value corresponds to two different $y$-values.
C. Yes, because every $x$-value corresponds to exactly one $y$-value.
D. No, because two of the $y$-values are the same.
Answer (1)
Check if each x -value corresponds to only one y -value.
Identify that x = 5 corresponds to two y -values, 2 and 5 .
Conclude that the table does not represent a function because one x -value has two different y -values.
The correct answer is B: No, because one x -value corresponds to two different y -values. B
Explanation
Checking the Definition of a Function To determine if the table represents a function, we need to check if each x -value corresponds to only one y -value.
Identifying the Issue Looking at the table, we see that when x = 5 , the table shows two different y -values: y = 2 and y = 5 . This means that the x -value of 5 is associated with two different y -values.
Concluding if it is a Function According to the definition of a function, each x -value must correspond to exactly one y -value. Since the x -value of 5 corresponds to two different y -values (2 and 5), the table does not represent a function.
Selecting the Correct Answer Therefore, the correct answer is B: No, because one x -value corresponds to two different y -values.
Examples
In real life, functions are used to model relationships between different quantities. For example, the amount of money you earn could be a function of the number of hours you work. Each hour worked corresponds to a specific amount of pay. If one hour could correspond to two different amounts of pay, the relationship would not be a function. This concept is crucial in various fields like economics, physics, and computer science, where accurate modeling of relationships is essential.
