Which of the following relations are functions? Choose all that apply. Assume that each different variable has a different value.
(1 point)
Responses
left braces left-parenthesis a comma b right-parenthesis comma left-parenthesis b comma a right-parenthesis comma left-parenthesis c comma c right-parenthesis comma left-parenthesis e comma d right-parenthesis right braces
left braces left-parenthesis c comma e right-parenthesis comma left-parenthesis c comma d right-parenthesis comma left-parenthesis c comma b right-parenthesis right braces
left braces left-parenthesis b comma b right-parenthesis comma left-parenthesis c comma d right-parenthesis comma left-parenthesis d comma c right-parenthesis comma left-parenthesis c comma a right-parenthesis right braces
left braces left-parenthesis a comma b right-parenthesis comma left-parenthesis b comma c right-parenthesis comma left-parenthesis c comma d right-parenthesis comma left-parenthesis d comma e right-parenthesis right braces
To determine if a relation is a function, we need to ensure that each input has only one corresponding output.
Looking at the options provided:
(1) The relation { (a, b), (b, a), (c, c), (e, d) } is a function because each input has a unique output.
(2) The relation { (c, e), (c, d), (c, b) } is not a function because the input c has multiple outputs.
(3) The relation { (b, b), (c, d), (d, c), (c, a) } is not a function because the input c has multiple outputs.
(4) The relation { (a, b), (b, c), (c, d), (d, e) } is a function because each input has a unique output.
Therefore, the functions are (1) and (4).