Which set of ordered pairs does not represent a function?{(6,1),(1,−6),(5,−6),(−1,−5)}{(−5,−1),(4,−2),(−4,5),(−6,5)}{(9,8),(−5,6),(6,5),(6,0)}{(−2,4),(9,−3),(4,−3),(2,8)}
Q. Which set of ordered pairs does not represent a function?{(6,1),(1,−6),(5,−6),(−1,−5)}{(−5,−1),(4,−2),(−4,5),(−6,5)}{(9,8),(−5,6),(6,5),(6,0)}{(−2,4),(9,−3),(4,−3),(2,8)}
Check Unique X-Values: To determine if a set of ordered pairs represents a function, we need to check if each input (x-value) maps to exactly one output (y-value). A function cannot have the same input mapping to different outputs.
Set 1: Determine Function: Let's examine the first set of ordered pairs: (6,1),(1,−6),(5,−6),(−1,−5). We need to check if any x-value is repeated with a different y-value. Looking at the x-values: 6, 1, 5, −1, we see that they are all unique. Since no x-value is repeated, this set represents a function.
Set 2: Determine Function: Now, let's examine the second set of ordered pairs: {(−5,−1),(4,−2),(−4,5),(−6,5)}. Again, we check for repeated x-values. Looking at the x-values: −5, 4, −4, −6, we see that they are all unique. Since no x-value is repeated, this set also represents a function.
Set 3: Determine Function: Next, let's examine the third set of ordered pairs: (9,8),(−5,6),(6,5),(6,0). We need to check for repeated x-values. Looking at the x-values: 9, −5, 6, 6, we notice that the x-value 6 is repeated. Since the x-value 6 maps to two different x1-values (x2 and x3), this set does not represent a function.
Set 4: Determine Function: Finally, let's examine the fourth set of ordered pairs: {(−2,4),(9,−3),(4,−3),(2,8)}. We check for repeated x-values. Looking at the x-values: −2, 9, 4, 2, we see that they are all unique. Since no x-value is repeated, this set represents a function.
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