Questions: Which of the following sets of ordered pairs defines a function? a. (6,2),(-9,-3),(2,-2),(3,-7) b. (2,4),(5,-8),(5,-9),(-8,2) Which sets of ordered pairs define a function? A. a and b B. a C. b D. Neither set of ordered pairs defines a function.

Solution Steps

To determine if a set of ordered pairs defines a function, we need to check if each input (first element of the pair) maps to exactly one output (second element of the pair). In other words, no two pairs should have the same first element with different second elements.

1. For set a, check if any first element is repeated with a different second element.
2. For set b, perform the same check as in step 1.

To determine if the set of ordered pairs \( a = \{(6,2),(-9,-3),(2,-2),(3,-7)\} \) defines a function, we check if each input (first element) is associated with exactly one output (second element).

• The inputs are \( 6, -9, 2, \) and \( 3 \).
• Each input is unique and maps to a unique output.

Since no input is repeated with a different output, set \( a \) defines a function.

For the set of ordered pairs \( b = \{(2,4),(5,-8),(5,-9),(-8,2)\} \), we perform the same check:

• The inputs are \( 2, 5, 5, \) and \( -8 \).
• The input \( 5 \) is repeated with different outputs \(-8\) and \(-9\).

Since the input \( 5 \) maps to two different outputs, set \( b \) does not define a function.

Final Answer