Which set of ordered pairs does not represent a function?{(−3,5),(−4,2),(−8,−1),(−6,5)}{(−8,3),(9,4),(8,1),(3,−2)}{(5,9),(3,−9),(−5,3),(3,−8)}{(9,−8),(−3,3),(−6,−3),(1,−8)}
Q. Which set of ordered pairs does not represent a function?{(−3,5),(−4,2),(−8,−1),(−6,5)}{(−8,3),(9,4),(8,1),(3,−2)}{(5,9),(3,−9),(−5,3),(3,−8)}{(9,−8),(−3,3),(−6,−3),(1,−8)}
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.
Check first set: Let's examine the first set: {(−3,5),(−4,2),(−8,−1),(−6,5)}. We need to check if any x-value is repeated with a different y-value.
Check second set: In the first set, all x-values are unique: −3, −4, −8, and −6. Since there are no repeated x-values, this set represents a function.
Check third set: Now, let's examine the second set: {(−8,3),(9,4),(8,1),(3,−2)}. Again, we check for any repeated x-values with different y-values.
Final decision: In the second set, all x-values are unique: −8, 9, 8, and 3. Since there are no repeated x-values, this set also represents a function.
Final decision: In the second set, all x-values are unique: −8, 9, 8, and 3. Since there are no repeated x-values, this set also represents a function.Next, let's examine the third set: {(5,9),(3,−9),(−5,3),(3,−8)}. We look for any repeated x-values with different y-values.
Final decision: In the second set, all x-values are unique: −8, 9, 8, and 3. Since there are no repeated x-values, this set also represents a function.Next, let's examine the third set: {(5,9),(3,−9),(−5,3),(3,−8)}. We look for any repeated x-values with different y-values.In the third set, the x-value 3 is repeated with different y-values: −82 and −83. This means that for the same input, there are two different outputs, which violates the definition of a function.
Final decision: In the second set, all x-values are unique: −8, 9, 8, and 3. Since there are no repeated x-values, this set also represents a function.Next, let's examine the third set: {(5,9),(3,−9),(−5,3),(3,−8)}. We look for any repeated x-values with different y-values.In the third set, the x-value 3 is repeated with different y-values: −82 and −83. This means that for the same input, there are two different outputs, which violates the definition of a function.Since the third set has a repeated x-value with different y-values, it does not represent a function. We do not need to check the fourth set, as we have already found the set that does not represent a function.
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