Hello there!
One way to determine if a relation or graph is a function is to check if any of the x values repeat themselves. If the x values repeat in any way, this would mean that the graph or relation is not a function.
Another way would be to use the vertical line test, which is only used on graphs. This is where you draw a vertical line through the graph and see if any points lay on that same line. If they do, that graph is not a function.
Using these things, we can apply it to find the correct answers:
a- this choice is a function since none of the x values of the coordinate pairs appear to repeat themselves.
b- this choice is also a function even though it appears that one of the x-values repeat. It would still be a function because the points (3,1) and (3,1) are the same point, which does not matter.
c- this choice is also a function since none of the x-values repeat themselves.
d-This is a function because if you were to draw a vertical line anywhere on the graph, none of the points would lay on the same line.
e- This is a function because if you were to draw a vertical line anywhere on the graph, none of the points would lay on the same line.
f- This is NOT a function because if you were to draw a vertical line, there would be points that would overlap on the same line.