Which set of ordered pairs does not represent a function?

Question

Answer
Multiple Choice Answers
left curly bracket, left parenthesis, 1, comma, minus, 8, right parenthesis, comma, left parenthesis, 8, comma, minus, 2, right parenthesis, comma, left parenthesis, minus, 7, comma, minus, 4, right parenthesis, comma, left parenthesis, minus, 7, comma, 3, right parenthesis, right curly bracket{(1,−8),(8,−2),(−7,−4),(−7,3)}
left curly bracket, left parenthesis, 8, comma, 3, right parenthesis, comma, left parenthesis, minus, 2, comma, minus, 8, right parenthesis, comma, left parenthesis, minus, 5, comma, minus, 8, right parenthesis, comma, left parenthesis, minus, 6, comma, minus, 5, right parenthesis, right curly bracket{(8,3),(−2,−8),(−5,−8),(−6,−5)}
left curly bracket, left parenthesis, minus, 2, comma, 4, right parenthesis, comma, left parenthesis, 9, comma, minus, 8, right parenthesis, comma, left parenthesis, 1, comma, minus, 4, right parenthesis, comma, left parenthesis, minus, 1, comma, minus, 4, right parenthesis, right curly bracket{(−2,4),(9,−8),(1,−4),(−1,−4)}
left curly bracket, left parenthesis, minus, 8, comma, minus, 3, right parenthesis, comma, left parenthesis, minus, 3, comma, 1, right parenthesis, comma, left parenthesis, 6, comma, minus, 3, right parenthesis, comma, left parenthesis, 4, comma, 0, right parenthesis, right curly bracket{(−8,−3),(−3,1),(6,−3),(4,0)}

Answer 1

To determine which set of ordered pairs does not represent a function, we need to remember that a function cannot have two different ordered pairs that have the same first element (or "x" value).

Let's analyze each option provided:

1. Set 1: \({(1,−8), (8,−2), (−7,−4), (−7,3)}\)

   • Here, the first element \(-7\) appears twice with different second elements \(-4\) and \(3\). Thus, this set does not represent a function.

2. Set 2: \({(8,3), (−2,−8), (−5,−8), (−6,−5)}\)

   • All first elements are unique, so this set does represent a function.

3. Set 3: \({(−2,4), (9,−8), (1,−4), (−1,−4)}\)

   • All first elements are unique, so this set also represents a function.

4. Set 4: \({(−8,−3), (−3,1), (6,−3), (4,0)}\)

   • All first elements are unique, so this set represents a function.

The only set that does not represent a function is Set 1: \({(1,−8), (8,−2), (−7,−4), (−7,3)}\).