Determine whether the relation shown here is a function. explain your answer. a) function, an input has 1 output b) function, an input has 2 different outputs c) function, no output has 2 different inputs d) not a function, an input has 2 different outputs

Option: D is the correct answer.

D) Not a function, an input has 2 different output.

Step-by-step explanation:

Function--

A function is a relation in which each element of first set is uniquely mapped to the element of the second set.

i.e. each element has a single image.

If there exist an element in a first set that is mapped to two different elements of the second set then it violates the definition or property of function.

So, from the given mapping we see that the element '2' in the first set is mapped to two different elements in the second set ( i.e. 2→ -4 and 2→ 5).

Hence, the given relation is not a function.

Hence, option: D is correct.