Which sets of ordered pairs represent functions from A to B? Explain.

A = {a, b, c} and B = {0, 1, 2, 3}

A. {(a, 1), (c, 2), (c, 3), (b, 3)}
B. {(a, 1), (b, 2), (c, 3)}
C. {(1, a), (0, a), (2, c), (3, b)}
D. {(c, 0), (b, 0), (a, 3)}

I narrowed it down to either B or C, but I'm not sure because they both don't use a letter or number twice as x. So I'm not sure which one is a function.

Ah, the joys of functions! Let's see if we can figure this out with a little laughter.

When it comes to functions, each input (represented by x) should have exactly one output (represented by y). In other words, each x in set A must be paired with only one y in set B. Now, let's take a closer look at the given sets of ordered pairs.

In option A, we have multiple outputs associated with the same input. Poor c is getting paired with both 2 and 3. It's like inviting two clowns with the same name to a party – a recipe for confusion!

Option B seems to be more promising. We have one pair for each element in set A, with no repetition. It's like throwing a party with a clown, a magician, and a juggler – a diverse and organized event!

Now, let's take a look at option C. While it's true that each input x is matched with a unique output y, the roles seem to be reversed. We have (1, a) and (0, a), which suggests that both a and b are getting mixed up. It's like having a clown who forgets their tricks and starts juggling in a magician's hat – a confusing and unpredictable act!

Lastly, option D has no pair for element b in set A. It's like trying to perform a comedy show without a clown – a sad and incomplete event!

So, after our analysis, the winner is option B: {(a, 1), (b, 2), (c, 3)}. It pairs each element from set A with a unique element from set B, making it a function that follows the rules without causing any chaos at the party!

To determine which sets of ordered pairs represent functions from A to B, we need to check if there is a unique output (y-value) for each input (x-value). In other words, we need to make sure that for each element in set A, there is only one corresponding element in set B.

Let's analyze each option:

A. {(a, 1), (c, 2), (c, 3), (b, 3)}
In this set, we can see that both (c, 2) and (c, 3) have the same input, which violates the definition of a function. Therefore, option A is not a function.

B. {(a, 1), (b, 2), (c, 3)}
In this set, each element in set A has a unique corresponding element in set B. Therefore, option B is a function.

C. {(1, a), (0, a), (2, c), (3, b)}
This set has the elements of A and B flipped, so it represents a function from B to A but not from A to B. Therefore, option C is not a function from A to B.

D. {(c, 0), (b, 0), (a, 3)}
In this set, each element in set A has a unique corresponding element in set B. Therefore, option D is a function.

Based on the above analysis, the sets of ordered pairs that represent functions from A to B are:

B. {(a, 1), (b, 2), (c, 3)}
D. {(c, 0), (b, 0), (a, 3)}

To determine which sets of ordered pairs represent functions from A to B, we need to examine the definition of a function.

A function is a relation between two sets where each element from the first set (the domain) corresponds to exactly one element in the second set (the codomain). In other words, each input can have only one output.

Let's check the given options:

A. {(a, 1), (c, 2), (c, 3), (b, 3)}
This set is not a function since the element 'c' in the domain corresponds to both 2 and 3 in the codomain. One element in the domain should be associated with only one element in the codomain.

B. {(a, 1), (b, 2), (c, 3)}
This set is a function since each element in the domain corresponds to a unique element in the codomain. For example, 'a' corresponds to 1, 'b' corresponds to 2, and 'c' corresponds to 3.

C. {(1, a), (0, a), (2, c), (3, b)}
This set is not a function because 'a' appears twice as the output and 1 is associated with both 'a' and 'b'. A proper function should have a unique output for each input.

D. {(c, 0), (b, 0), (a, 3)}
This set is a function since each element in the domain corresponds to a unique element in the codomain. 'c' corresponds to 0, 'b' corresponds to 0, and 'a' corresponds to 3.

Based on this analysis, the answer is B. {(a, 1), (b, 2), (c, 3)}. It is the only set where each element in the domain corresponds to a unique element in the codomain, satisfying the definition of a function.

to be a function, each member of A must map to a single member of B.

A is not a function: c-->2 and c-->3
B is
C is not, since it does not map A onto B
D is