Which set of ordered pairs does not represent a function?{(−2,5),(6,−1),(−7,5),(−6,4)}{(2,−4),(−7,9),(7,8),(3,8)}{(3,−1),(3,7),(0,−3),(−4,−5)}{(8,−5),(−5,−1),(1,−5),(−7,5)}
Q. Which set of ordered pairs does not represent a function?{(−2,5),(6,−1),(−7,5),(−6,4)}{(2,−4),(−7,9),(7,8),(3,8)}{(3,−1),(3,7),(0,−3),(−4,−5)}{(8,−5),(−5,−1),(1,−5),(−7,5)}
Define function as relation: A function is defined as a relation where each input ( extit{x}-value) has exactly one output ( extit{y}-value). To determine which set of ordered pairs does not represent a function, we need to check if there are any repeated extit{x}-values with different extit{y}-values in each set.
Examine first set: Let's examine the first set: {(−2,5),(6,−1),(−7,5),(−6,4)}. We need to check if any x-value is repeated with a different y-value. (−2,5) and (−7,5) have different x-values, so they are fine. (6,−1) and (−6,4) also have different x-values. There are no repeated x-values with different y-values in this set.
Examine second set: Now, let's examine the second set: (2,−4),(−7,9),(7,8),(3,8). Again, we check for repeated x-values with different y-values.(2,−4), (−7,9), (7,8), and (3,8) all have unique x-values. There are no repeated x-values with different y-values in this set.
Examine third set: Next, we examine the third set: {(3,−1),(3,7),(0,−3),(−4,−5)}. Here, we immediately see that the x-value 3 is repeated with different y-values: −1 and 7.(3,−1) and (3,7) indicate that the same x-value has two different y-values, which violates the definition of a function.
Examine fourth set: Finally, let's examine the fourth set: (8,−5),(−5,−1),(1,−5),(−7,5). We check for repeated x-values with different y-values.(8,−5), (−5,−1), (1,−5), and (−7,5) all have unique x-values. There are no repeated x-values with different y-values in this set.
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