Question

What is the domain of the following relation? Is it a function? R: {(1,2), (2,2), (-1, -2), (-3, 4)}

a) {-2, 2, 4} not a function because output values are not repeating
b) {-3,-1, 1, 2} not a function because the input values are not repeating
c) {-3,-1, 1, 2} is a function because there are no repeating input values
d) {-2, 2, 4} is a function because there are repeating output values.

Answer 1

The domain of the given relation R is {-3, -1, 1, 2} and it is a function because each input value is paired with only one output value, satisfying the definition of a function.

Step-by-step explanation:

The domain of a relation or function consists of all the first elements (called inputs, or x-values) in the ordered pairs. For the relation R: {(1,2), (2,2), (-1, -2), (-3, 4)}, the domain is {-3, -1, 1, 2}, which represents the set of all input values. To determine if this relation is a function, we check if each input value is paired with exactly one output value (y-value). In R, no input value is repeated, which means it satisfies the definition of a function. Therefore, the correct answer is 'c) {-3, -1, 1, 2} is a function because there are no repeating input values.'