Question

Which of the following relations are functions? If it is a function determine its domain and range.
i) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14,7)}
ii) {(0, 0), (1, 1), (1, -1), (4, 2), (4, -2), (9, 3), (9, -3), (16, 4), (16, -4)}
iii) {(2, 1), (3, 1), (5, 2)}

Answer 1

Answer:

i) & ii)  are functions

Step-by-step explanation:

i) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14,7)}

f(x) = 2 * x

Domain =   1 ≤ x ≤ 7  x∈Z

Range = 2 ≤ x ≤ 14  x∈Z

ii) {(0, 0), (1, 1), (1, -1), (4, 2), (4, -2), (9, 3), (9, -3), (16, 4), (16, -4)}

f(x) = x²

Domain =   -4 ≤ x ≤ 4  x∈Z

Range = 0 ≤ x ≤ 16  x∈Z

iii) {(2, 1), (3, 1), (5, 2)}

not a function

Answer 2

Answer:-

Option i) and ii) are relation

Step-by-step explanation:

In this question,

Which of the following is a function?

A function is a relation, for each input there is a unique output.

i) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}

f(X) = 2X         X ∈ [1,7]

Therefore Domain = 1≤X≤7    where X∈Z

                 Range = 2 ≤ X ≤ 14  where X∈Z

ii) {(0,0), (1,1), (1,-1), (4,2), (4,-2), (9,3),(9,-3),(16,4),(16,-4)}

f(X) = X²

Domain =   -4 ≤ X ≤ 4  X∈Z

Range = 0 ≤ X ≤ 16  X∈Z

iii) {(2,1), (3,1), (5,2)}

This is not a relation

As image for 2 is 1

and for 3 image is also 1