Question

State, giving reason, whether each of the following diagrams represent a function or not.

Answer 1

Hint: In this diagram the column \[A\] represents input value of the relation and column \[B\] represents the output value. When we join an element of column \[A\] with column \[B\] then those elements are the respective input and output of the relation. Since the function is a relation which gives only one output within all over the domain. Means if any of the input values has two different outputs then it's not a function. In this figure as shown, the element \[a\] has three outputs \[1,2,3\]. Hence it is not a function.

Complete answer:
As we are given a relation with input in column \[A\] and their respective output is in column \[B\]
We know that function is a relation from the set of inputs to a set of possible outputs where each input is related to exactly one output.
As in this given question, the column \[A\] has \[3\] elements \[a,b,c\] and the element \[a\] of the input set has three outputs \[1,2,3\].
Thus, it fails the definition of function
Hence it is not the function

Note:
In this question, the given relation between \[A\] and \[B\] is not a function as one of its input values has more than one different output value. Function is a binary relation between two sets where every element of the first set is associated with exactly one element of another set. Means if in a binary relation if all the elements in the input set are not connected with any output then it is not a function.