Question

Is the following relation a function?

(i) R1 = {(2, 3), (1/2 ,0), (2, 7), (– 4, 6)}

(ii) R2 = x is a real number A) Both R1 and R2 are functions.
B) Only R1 is a function.
C) Only R2 is a function.
D) Neither R1 nor R2 are functions.

Answer 1

The relation R1 is not a function because it has the same input with two different outputs, whereas R2 is a function because each real number as input is associated with exactly one output (its absolute value).

Step-by-step explanation:

The question asks whether the given relations R1 and R2 are functions. By definition, a relation is a function if each input is associated with exactly one output. In other words, in a set of ordered pairs, there can be no two pairs with the same first element but different second elements.

Looking at R1, we find the ordered pairs (2, 3) and (2, 7). This shows that the same input (2) gives two different outputs (3 and 7), which violates the definition of a function. Hence, R1 is not a function.

The relation R2 represents the set of all ordered pairs where the first element is a real number and the second element is the absolute value of the first element. Since for every real number x, there is exactly one absolute value, each input x is associated with exactly one output |x|. Thus, R2 is a function.

Therefore, the correct answer is Only R2 is a function.