Question

"Which of the following sets of ordered pairs represents a function?

P = {(6, –7), (3, –2), (–9, 2), (–5, –7)}

Q = {(–7, 8), (4, –6), (–3, 1), (1, 5)}

A) Only P
B) Only Q
C) Both P and Q
D) Neither P nor Q"

Answer 1

Both sets P and Q represent functions because in both sets, each input (the first element of the ordered pairs) is associated with exactly one output (the second element), with no repetition of input values.

Step-by-step explanation:

To determine which set of ordered pairs represents a function, you need to check for uniqueness in the first elements of the pairs, commonly known as the 'domain' of the function.

Each input (first element of the ordered pair) must be associated with exactly one output (second element) for the set to qualify as a function.

Looking at set P = {(6, –7), (3, –2), (9, 2), (–5, –7)}, you can see that each first element is unique; no input value (x-coordinate) is repeated. Therefore, each input has only one output associated with it. Set P represents a function.

In set Q = {(7, 8), (4, –6), (3, 1), (1, 5)}, like set P, there is no repeating x-value. Thus, set Q also represents a function where each input has one unique output value.

The correct answer is C) Both P and Q.