Question

Which of the following relations is a function?

Select all that apply.
A{(1,3),(2,4),(3,5),(4,6),(5,7)}
B{(3,1),(4,1),(5,1),(6,1),(7,1)}
C{(1,0),(1,2),(3,2),(5,4),(7,6)}
D {(-5,4),(-3,2),(-1,0),(-3,-2).(-5,-4)}

Answer 1

Relation A and B are functions because each input value has a unique output value. Relation C and D are not functions because some input values have multiple output values.

Step-by-step explanation:

A function is a relation between two sets in which each input value is assigned to exactly one output value. To determine if a relation is a function, we need to check if each input value has a unique output value. In this case, relation A {(1,3),(2,4),(3,5),(4,6),(5,7)} is a function because each input value corresponds to a unique output value. Relation B {(3,1),(4,1),(5,1),(6,1),(7,1)} is also a function because each input value has the same output value. However, relation C {(1,0),(1,2),(3,2),(5,4),(7,6)} is not a function because the input value 1 has two different output values, 0 and 2. Relation D {(-5,4),(-3,2),(-1,0),(-3,-2),(-5,-4)} is also not a function because the input value -3 has two different output values, 2 and -2.