Which sets of ordered pairs represent functions from A to B? (Select all that apply.)
A = {3, 4, 5, 6} and B = {−2, −1, 0, 1, 2}
{(3, 2), (6, 0), (4, 1)}
{(3, −1), (5, 2), (4, −2), (6, 0), (4, 1)}
{(3, 1), (4, −2), (5, 0), (6, 2)}
{(3, 0), (4, 0), (5, 0), (6, 0)}
if each x-value is used only once, then it is a function
Would the last option count because it would be y=0x?
To determine which sets of ordered pairs represent functions from A to B, we need to check if each element in set A is paired with only one element in set B.
Let's go through each option:
1. {(3, 2), (6, 0), (4, 1)}: In this set, each element in A is paired with only one element in B. So, this set represents a function from A to B.
2. {(3, −1), (5, 2), (4, −2), (6, 0), (4, 1)}: Here, we can see that the element 4 in A is paired with two different elements in B, -2 and 1. Therefore, this set does not represent a function from A to B.
3. {(3, 1), (4, −2), (5, 0), (6, 2)}: In this set, each element in A is paired with only one element in B. So, this set represents a function from A to B.
4. {(3, 0), (4, 0), (5, 0), (6, 0)}: Here, all the elements in A are paired with the same element in B, 0. While this can represent a valid function, it would be a constant function rather than a distinct mapping for each element. So, although this set represents a function, it is not considered a unique function from A to B.
Therefore, the sets that represent functions from A to B are: {(3, 2), (6, 0), (4, 1)} and {(3, 1), (4, −2), (5, 0), (6, 2)}.