Answer:
Table B
Step-by-step explanation:
we are given 4 tables and we want to find the table that represents a function.
well recall, The conditions of a relation to be a function
A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties:
- For every element x in A, there is an element y in B such that (x, y) ∈ F.
- For all elements x in A and y and z in B if (x, y) ∈ F and (x,z) ∈ F, then y = z.
more precisely,if F is a function from a set A to a set B, then given any element x in A, property (1) from the function definition guarantees that there is at least one element
of B that is related to x by F and property (2) guarantees that there is at most one such
element.
at first rewrite the input and output of Table A,B ,C and D as ordered pairs
[tex]A = \{(5,3),(5,2),(4,1) \}[/tex]
[tex]B= \{(1,2),(3,2),(5,3) \}[/tex]
[tex]C = \{(0,0),(1,2),(1,3) \}[/tex]
[tex]D= \{(4,2),(4,3),(4,4) \}[/tex]
Table A,C & D:
Table A, C and D does not represent a function because it does not satisfy property (2). The ordered pairs (5, 3) and (5, 2) in A, (1,2) and (1,3) in C and (4,2),(4,3),(4,4) have the same first element but different second elements.
Table B:
Table B represents a function: Each inputs {1, 3, 5} is related to some outputs {2, 2, 3} and no inputs {1, 3, 5} is related to more than one outputs {2, 2, 5}.
hence, it's our answer
