Is the following relation a function? If not, why?
{(Juan, escuela), (Mariposa, escuela), (Fernando, casa), (Maria, tienda)}
Answer
This is a function. A very Spanish one.
{(Juan, escuela), (Mariposa, escuela), (Juan, casa), (Maria, tienda)}
This is not a function, because Juan is being paired with both escuela and casa. Unless he is being home-schooled, or casa-escuela'd, ain't no way.
{(1, 1), (1, 2), (1, 3)}
This is not a function, because 1 is being paired with 1, 2, and 3 all at once.
{(1, 1), (1, 1), (2, 3)}
This is a function. Remember, in sets we only need to list each element once. So
{(1, 1), (1, 1), (2, 3)} = {(1, 1), (2, 3)}
which is a function.
y = 3x2 + 4
This is a function.
x = |y|
This is not a function. For example, the ordered pairs (1, 1) and (1, -1) are both in this relation.
x = y2 where y is positive.
This is a function, because now ordered pairs such as (4, -2) aren't in the relation.
x2 = y2
This is not a function. For example, this relation contains the ordered pairs (1, 1) and (1, -1).
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