Answer
See below.
Work Step by Step
$\text{The graph of a real-valued function of a real variable.}$
A function of a real variable has, as its domain, the set of real numbers, or one of its subsets.
To each value x from the domain, exactly one real number f(x) is assigned.
Plotting the points (x,f(x)), we obtain the graph of the function f.
So, to answer the first question, the graph of f is the set of points in the coordinate plane with coordinates (x,f(x)).
$\text{The vertical line test.}$
When graphing a relation f, we plot points (x,f(x)).
A relation is a function if "EXACTLY one output f(x) is assigned to EACH input x."
If we obtain two or more points on the graph with the same x-coordinate, but with different y-coordinates, then the graph can not represent a function, because there are cases where more outputs are assigned to one input.
Thus, if every vertical line intersects the graph in at most one point on the graph, then the graph can represent a function. We say that in this case, that the graph passes the vertical line test.
If we can find a vertical line that intersects the graph in more than one point, the graph fails the test and can not represent a function.
