Which of the following relations is not a function? (K:1)

Question

BlackTom AI · Accepted Answer

Here is a step-by-step examination of each option to determine which relation fails to be a function.
Option a: {(−2,1), (−1,1), (0,1), (1,1), (2,1)}. Each x-value (input) appears exactly once with its corresponding y-value. Although all outputs are the same, a function only requires that every input has a single output, which holds here. Therefore, this relation is a function.
Option b: {(−2, 1), (−1, 2), (0,4), (1,1), (2,2)}. All the x-values are distinct: −2, −1, 0, 1, 2. Each input maps to one output, so this is a function as well. There are no multiple y-values for the same x.
Option c: {(4,5), (8,9), (1,2), (0,0), (9,4)}. Again, every x-value is unique: 4, 8, 1, 0, 9. Each input has a single corresponding output, so this is a function.
Option d: {(−5, 4), (−3,8), (1,4), (2,7), (−5,9)}. Here, the x-value −5 appears twice, paired with two different y-values (4 and 9). A function cannot assign more than one output to the same input, so this relation violates the definition of a function. The repeated x-value with distinct outputs shows it is not a function.
In summary, options a, b, and c each adhere to the definition of a function by ensuring every input has a single output, whereas option d does not because of the repeated input −5 associated with two different outputs.

Which of the following relations is not a function? (K:1)

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