By definition, a set of values can be considered a function if every value of x (input) corresponds to one value of y (output)
If at least one input has two outputs or more, then the set cannot be considered a function.
With this in mind, we have to analyze each graph to determine if it corresponds to a function or not.
Graph A.
In this graph, we can see one curve that starts at the origin (0,0) and continues towards +∞
For every value of x determined there is only one value of y.
This means that this graph corresponds to a function.
Graph B
This graph has three horizontal lines, if you look, for the values of x=-2 and x=-1 the first two lines overlap, which means that this graph for x=-2 corresponds to the values y=3 and y=1.
The same happens with the second and third line, for the values of x=0 and x=1 both lines overlap so that each value of x has two corresponding values of y, y=1, and y=-1
This graph does not correspond to a function.
Graph C
This graph also has three parts or steps but they don't overlap each other.
For the values of x from -5 to -3, there is only one value of y, y=-1
For the values of x from -1 to 1, there is only one value of y, y=1
For the values of x from 3 to 5, there is only one value of y, y=3
This means that this graph corresponds to a function.
Graph D
This graph shows a V-shaped, there are no lines overlapping each other, which indicates that every value of x corresponds to only one value of y.
This means that this graph corresponds to a function.
The only graph that does not correspond to a function is B.
