Question

A function is defined by the set of ordered pairs {(-2,3),(-1,4),(0,5)}. Which ordered pair below, if added to this set, would create a set that no longer represents a function.
1) (1,5)
2) (3,-2)
3) (-1,-4)
4) (-4,-1)

Answer 1

Answer: 3) (-1,-4)

Step-by-step explanation:

We define a function as a relationship that maps elements from one set (inputs) into elements of another set (outputs).

The functions have one important rule, each element in the domain (the set of possible inputs) can be mapped into only one element in the range (set of possible outputs).

Then if we have:

a ≠ b

and for an input x0.

f(x0) = a

and

f(x0) = b

this is not a function, as it maps the value x0 into two different values.

Then we know that the points  {(-2,3),(-1,4),(0,5)} define our function.

Then the option that makes this relation to not be a function, will be any point that has the same input as some of the above ones, and different output.

the correct one is 3) (-1, -4)

Then the set will be:

{(-2,3),(-1,4),(0,5), (-1, -4)}.

Now we have two times the input -1, and different outputs, then this is not a function.