Answer:
(C) II and III only
Step-by-step explanation:
Given
[tex]I. \{(0, 0), (0, 1), (0, 2)\}[/tex]
[tex]II. \{(0, 0), (1, 1), (2, 4)\}[/tex]
[tex]III. \{(0, 0), (1, 2), (2, 2)\}[/tex]
[tex]IV.\ {(0, 0), (1, 2), (1, 3)\}[/tex]
Required
Which is a function?
A relation is of the form [tex]\{(x_1,y_1),(x_2,y_2),(x_2,y_2),(x_2,y_2).........(x_n,y_n)\}[/tex]
Where [tex]x = domain[/tex] and [tex]y = range[/tex]
And for a relation to be regarded as a function, all its x values must be unique. i.e. unrepeated.
Analyzing the options
[tex]I. \{(0, 0), (0, 1), (0, 2)\}[/tex]
This is not a function because 0 in multiple times for different y values (range)
i.e. (0,0), (0,1) and (0,2)
[tex]II. \{(0, 0), (1, 1), (2, 4)\}[/tex]
This is a function because each of the x values (domains) are unique for different y values (range)
[tex]III. \{(0, 0), (1, 2), (2, 2)\}[/tex]
This is a function because each of the x values (domains) are unique for different y values (range)
[tex]IV.\ {(0, 0), (1, 2), (1, 3)\}[/tex]
This is not a function because 1 in multiple times for different y values (range)
i.e. (1,2) and (1,3)
