Definition of a function
For something to be considered a function, any given x-value must yield exactly ONE (1) y-value.
How to check this
If, in the graph, you can find an x-value that has more than 1 corresponding y-value, it's not a function.
Note: a function can still have multiple x-values give the same y-value.
Checking our graphs against the definition
Graph 1:
The x-value of -3 gives an infinite number of y-values. Since infinity is more than 1, it's not a function.
Graph 2:
There are no x-values in this graph which give more than 1 y-value. Note that each y-value except for 0 has 2 x-values which give that value.
For example, both x = 0 and x = 2 give y = 3.
However, it can still be called a function, remember:
a function can still have multiple x-values give the same y-value
Graph 3:
Every x-value greater than -3 has several corresponding y-values. Thus, it's not a function.
Graph 4:
All x-values greater than 1 and smaller than -1 have multiple corresponding y-values. Thus, it's not a function.
Answer
The only graph that fulfills the definition of a function is graph 2, so that is the graph which represents a function!
