A function takes one element (the input) from the domain set and maps it to exactly one element (the output) in the range set.
For example, suppose the domain is {1, 2, 3} and the range is {4, 5}.
This is a function:
{1 => 4, 2 => 4, 3 => 5}
because for each input, there is only one output.
This is not a function:
{1 => 4, 1 => 5, 2 => 4}
because 1 is mapped to more than one output.
From the 8 given relations, we have
functions: 1, 3, 4, 6, 7
not functions: 2, 5, 8
Relations 2, 5, and 8 are not functions because
• (2) 9 is mapped to both 6 and 8
• (5) 2 is mapped to both 0 and 8
• (8) 9 is mapped to both 2 and 7
For diagrams like this, the thing to look for is multiple line segments starting from one input in the domain set.