Which of the following relations is a function?
A. {(5, 2), (3, 2), (4, 2), (5, 1)}
B. {(1, 2), (1, 3), (2, 1), (3, 4)}
C. {(1, 3), (2, 6), (3, 8), (1, 7)}
D. {(1, 4), (8, 9), (10, 11), (12, 12)}
I say c
If for every x, there is one and only one value of y, we have a function
in your c)
I see 1 --->3
and 1 ----> 7
oops, contradiction!
same is true for a and b
mmmmhhh, look carefully at D
in b, x=1, y=2 or 3 not a function
in c, x=1, y=3 or 7, not a function
In a, x=5, y can be two values. not a function
in d. each x has a related unique y.
To determine if a relation is a function, we need to check for any repetitions of the same input value (first element of each ordered pair) with different output values (second element of each ordered pair). If there are no repetitions, then the relation is a function.
Let's analyze each option:
A. {(5, 2), (3, 2), (4, 2), (5, 1)}
In this relation, we have repetitions of the input value 5 with different output values (2 and 1). Therefore, it is not a function.
B. {(1, 2), (1, 3), (2, 1), (3, 4)}
Similar to option A, here we have repetitions of the input value 1 with different output values (2 and 3). Consequently, it is not a function.
C. {(1, 3), (2, 6), (3, 8), (1, 7)}
In this relation, we have a repetition of the input value 1 with different output values (3 and 7). As a result, it is not a function.
D. {(1, 4), (8, 9), (10, 11), (12, 12)}
In this relation, there are no repetitions of input values, meaning each input value has a unique output value. Therefore, it is a function.
Based on the analysis, the correct answer is D. {(1, 4), (8, 9), (10, 11), (12, 12)}.