The relation will be a function if x not repeated
You can check any graph by drawing a vertical line in different positions, if the vertical line crosses the graph in more than one point, then it is not a function
Look at the first figure
there are some points
If you draw a vertical line passes through them
One point lies on each vertical line
So the first graph is a function
The second graph is a vertical line means all the points on it have the same x-coordinate, then x repeated many times, so
It can not be a function because x never repeated in the function
The third figure is a circle, if you draw a vertical line passing through it, it will cross it in two points, then it is not a function
The fourth figure has two arrows go from x = 0, which means x is repeated, so it's not a function
The fifth figure has two points with the same x coordinate, then it is not a function
The sixth figure is a function because just 1 arrow goes from each x (y can be repeated)
In the table x has different numbers means the table represents a function
In the set of ordered pairs, each x appears just one time, then it is a function
The last graph is a function because any vertical line will cut it in just one point