Determine whether the following relation represents a function. Give the domain and range for the relation. [tex] \lbrace(-1,4),(-8,9),(2,2),(9,9)\rbrace [/tex] Does the given relation represent a function?
Yes
No
Answer (2)
The relation {( − 1 , 4 ) , ( − 8 , 9 ) , ( 2 , 2 ) , ( 9 , 9 )} is a function since each x-value has a unique y-value. The domain is { − 1 , − 8 , 2 , 9 } and the range is { 2 , 4 , 9 } . Therefore, the answer to the question is Yes.
;
The relation is a function because each x-value has only one corresponding y-value.
The domain is the set of all x-values: { − 1 , − 8 , 2 , 9 } .
The range is the set of all y-values: { 2 , 4 , 9 } .
The relation represents a function, and its domain and range are { − 1 , − 8 , 2 , 9 } and { 2 , 4 , 9 } , respectively. The answer to the question 'Does the given relation represent a function?' is Yes. Y es
Explanation
Understanding the Problem We are given the relation as a set of ordered pairs: {( − 1 , 4 ) , ( − 8 , 9 ) , ( 2 , 2 ) , ( 9 , 9 )} . We need to determine if this relation represents a function, and if it does, we need to find its domain and range. A relation is a function if each x-value is associated with only one y-value.
Checking if the Relation is a Function To check if the relation is a function, we examine the x-values in the ordered pairs. The x-values are -1, -8, 2, and 9. Since none of these x-values are repeated, each x-value is associated with only one y-value. Therefore, the relation is a function.
Finding the Domain The domain of the function is the set of all x-values in the ordered pairs. So, the domain is { − 1 , − 8 , 2 , 9 } .
Finding the Range The range of the function is the set of all y-values in the ordered pairs. So, the range is { 4 , 9 , 2 , 9 } . Since we only list unique values in a set, the range is { 2 , 4 , 9 } .
Final Answer The relation represents a function. The domain is { − 1 , − 8 , 2 , 9 } and the range is { 2 , 4 , 9 } .
Examples
Functions are used everywhere in real life. For example, the price of an item is a function of the sales tax. The amount of your paycheck is a function of the number of hours you work. The distance a car travels is a function of time and speed. In this case, we can think of the relation as a function that maps a set of inputs (x-values) to a set of outputs (y-values).
