Which of the following lists of ordered pairs is a function?
A. $(0,2),(2,3),(0,-2),(4,1)$
B. $(2,4),(0,2),(2,-4),(5,3)$
C. $(1,6),(2,7),(4,9),(0,5)$
D. $(1,2),(1,-2),(3,2),(3,4)$
Answer (1)
A function is a relation where each x-value has only one y-value.
List A has x-value 0 paired with both 2 and -2.
List B has x-value 2 paired with both 4 and -4.
List C has each x-value paired with only one y-value, so it is a function. The final answer is C .
Explanation
Understanding the Definition of a Function We need to determine which of the given lists of ordered pairs represents a function. A function requires that each input (x-value) has only one output (y-value). In other words, no x-value can be paired with two different y-values.
Checking Each List Let's examine each list:
List A: ( 0 , 2 ) , ( 2 , 3 ) , ( 0 , − 2 ) , ( 4 , 1 ) . The x-value 0 appears twice, paired with 2 and -2. This violates the definition of a function.
List B: ( 2 , 4 ) , ( 0 , 2 ) , ( 2 , − 4 ) , ( 5 , 3 ) . The x-value 2 appears twice, paired with 4 and -4. This violates the definition of a function.
List C: ( 1 , 6 ) , ( 2 , 7 ) , ( 4 , 9 ) , ( 0 , 5 ) . Each x-value (1, 2, 4, 0) is paired with only one y-value. This satisfies the definition of a function.
List D: ( 1 , 2 ) , ( 1 , − 2 ) , ( 3 , 2 ) , ( 3 , 4 ) . The x-value 1 appears twice, paired with 2 and -2. The x-value 3 appears twice, paired with 2 and 4. This violates the definition of a function.
Identifying the Function Only List C satisfies the definition of a function, where each x-value has a unique y-value.
Examples
Functions are used everywhere in real life! For example, the price of an item is a function of the item itself. Each item has one specific price. Another example is the assignment of students to seats in a classroom; each student sits in one specific seat. Understanding functions helps us model and analyze these relationships.
