1.
(04.01)
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Only A
Only B
Both A and B
Neither A nor B
Only B
Well, well, well, let's see if we can function our way through this question! A function is a relationship where each input has only one unique output. So, let's take a look at each set of ordered pairs.
In set A, we have (-5, 5), (-2, 2), (2, -2), and (5, -5). Guess what? Each input (the first number in each pair) has only one output (the second number in each pair). So, A is a function!
Now, onto set B. We have (4, 2), (3, -2), (9, 4), and (11, -3). Hocus pocus, all the inputs in set B also have only one output. So, B is also a function!
To sum it up, both set A and set B represent functions. Time to celebrate, we've found ourselves a matching pair!
To determine if a set of ordered pairs represents a function, we need to check if each input (x-coordinate) maps to a unique output (y-coordinate). In other words, there should be no repeated x-coordinates in the set.
Let's analyze each set of ordered pairs:
A = {(-5, 5), (-2, 2), (2, -2), (5, -5)}
In set A, each input value (-5, -2, 2, and 5) has a unique output value (5, 2, -2, and -5). Therefore, set A represents a function.
B = {(4, 2), (3, -2), (9, 4), (11, -3)}
In set B, each input value (4, 3, 9, and 11) also has a unique output value (2, -2, 4, and -3). Therefore, set B also represents a function.
Since both set A and set B have no repeated x-coordinates, the answer is:
Both A and B
if a relation is a function, no x-value may be used twice.
So look at A and B and check to see whether any x value is repeated. If not, then it is a function.