Select the correct answer.
Which of the following sets of ordered pairs represents a function?
A. {(-9,9), (-9,12), (-9,0), (12,-9)}
B. {(9,14), (9,4), (0,0), (11,16)}
C. {(0,-9), (14,-9), (0,9), (-9,14)}
D. {(9,-9), (12,-9), (0,-9), (-9,12)}
Answer (2)
A function requires each x-value to have only one corresponding y-value.
Set A has -9 associated with 9, 12, and 0, so it's not a function.
Set B has 9 associated with 14 and 4, so it's not a function.
Set C has 0 associated with -9 and 9, so it's not a function.
Set D has each x-value associated with only one y-value, thus it is a function. D
Explanation
Understanding the Definition of a Function A function is a relation where each element of the domain (the first element in the ordered pair) is associated with exactly one element of the range (the second element in the ordered pair). We need to determine which of the given sets of ordered pairs represents a function.
Analyzing Each Set of Ordered Pairs Let's examine each set of ordered pairs:
Set A: {(-9,9), (-9,12), (-9,0), (12,-9)}. Here, the x-value -9 is associated with three different y-values (9, 12, and 0). Therefore, this set does not represent a function.
Set B: {(9,14), (9,4), (0,0), (11,16)}. Here, the x-value 9 is associated with two different y-values (14 and 4). Therefore, this set does not represent a function.
Set C: {(0,-9), (14,-9), (0,9), (-9,14)}. Here, the x-value 0 is associated with two different y-values (-9 and 9). Therefore, this set does not represent a function.
Set D: {(9,-9), (12,-9), (0,-9), (-9,12)}. Each x-value is associated with only one y-value. Therefore, this set represents a function.
Conclusion Based on our analysis, only set D represents a function because each x-value is associated with 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 you work and the amount of money you earn can be represented by a function. If you work a certain number of hours, the function will tell you exactly how much money you will earn. Similarly, the relationship between the temperature of an oven and the time it takes to bake a cake can be represented by a function. Knowing these relationships helps us make predictions and understand how different things are connected.
Only Set D represents a function because each x-value is associated with exactly one y-value. The other sets have x-values paired with multiple y-values, which violates the definition of a function. Thus, the correct answer is D.
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