Answer:
First, let's do a fast definition of a function.
A function is a relation that maps elements from a given set (the domain, is the set of the inputs, usually represented with the variable x) into elements of another set (the range, which is the set of the outputs, usually represented with the variable y)
The functions can map each element of the domain into only one output.
Now, let's solve the problem:
For the vertical table, we can see that the values of x are:
{1, 2, 3} This is the domain.
And the values of y are:
{4, 6, 8} This is the range.
This relation represents a function.
For the horizontal table, we can see that:
The inputs are:
{4, 5} (notice that the 4 is two times there) This is the domain.
And the outputs are:
{2, 3, 4} This is the range.
Here we can see that this relationship maps the input "4" into two different outputs, then this is not a function.
2) We want to know if the graph represents a function.
The first thing we can see is that if we draw a vertical line in some places, the line will touch the graph at two different points. This means that one single value of x can be mapped into two different values of y.
And as we already said, a function maps each input into only one output, then the graph does not represent a function.
