Select the relation that is a function.
a.
{(21, 11), (21, 10), (21, 9), (21, 8)}
c.
{(-6, -5), (3, 2), (10, 8), (3, 3)}
b.
{(-2, -1),(5, -1), (16, 3), (-3, -9)}
d.
{(5, 10), (-3, 10), (-3, -10), (4, 7)}
hint: each element must have a single image.
Just tell the answer
cause i don't understand what you saying
Note that in (a) (21,11) and (21,10) indicate that f(21) = 11 and f(21) = 10.
That can't be so, for a function.
In (c), we have f(3) = 2 and f(3) = 3
In (b) there is only one mapping for each element.
In (d) we have f(-3)=10 and f(-3)=-10.
each element can have only one image under the mapping. That is, the relation maps the first value to the second value in each pair.
A value can only be mapped to a single image. Better study the chapter on relations, mapping, images, etc. and what makes a function more restrictive than just a general relation.
so b?
That'd be my guess, unless you have b and c switched. They are listed out of order.
To determine if a relation is a function, we need to see if each input (x-value) is associated with exactly one output (y-value).
For option a:
{(21,11), (21,10), (21,9), (21,8)}
In this relation, the input 21 is associated with multiple outputs (11, 10, 9, 8). Therefore, option a is not a function.
For option c:
{(-6,-5), (3,2), (10,8), (3,3)}
Again, we can see that the input 3 is associated with multiple outputs (2, 3). Therefore, option c is not a function.
For option b:
{(-2,-1), (5,-1), (16,3), (-3,-9)}
In this relation, each input is associated with exactly one output. Therefore, option b is a function.
For option d:
{(5,10), (-3,10), (-3,-10), (4,7)}
Here, the input -3 is associated with multiple outputs (10, -10). Therefore, option d is not a function.
So, the correct answer is option b.