Answer: A function is always a relation.
Explanation:
We know that a relation is said to be a function, if for every input value (independent variable-x) there is only one unique (dependent variable -y).
Let's check all the statements:
A function is always a relation.
→ It is true, each and every function is a relation but not evry relation is a function.
A function is a relation, if and only if, the x-values do not repeat in a given set.
→Every function is a relation, so there is no such condition to be a relation.
A relation is a function, if and only if, the x- values do not repeat in a given set.
→ It is not true, x-values can be repeated but the corresponding y-values must remains same.
A function is never a relation.
→ It is not true by the definition of function.
A relation is never a function.
→ It is not true by the definition of function.