Sanity check, is $\{(-9,-3),(2,-1),(7,7),(-1,-1)\}$ a function?  EDIT#2: Yes, I'm crazy! This IS a function. Thanks for beating the correct logic into me everyone!
I'm using a website provided by my algebra textbook that has questions and answers. It has the following question: 
Determine whether the following relation represents a function:
$$\{(-9,-3),(2,-1),(7,7),(-1,-1)\}$$
I answered NO, it is not a function but the website says it is. Am I wrong? If so, what am I missing?
EDIT: I was given the following definition in class: 

Function: A function is a rule which assigns to each X, called the domain, a unique y, called the range. 

My instructor also said that if you plot the points you can tell if it is not a function if it fails the vertical line test. Here is the graph of the above points, and for example it would fail the vertical line test if I drew one on x = 1, right?

Thanks!
Jason
 A: A function doesn't have to be from $\mathbb R$ to $\mathbb R$. The domain of a function can be as simple a set as $\{-9,-1,2,7\}$.
A: A function cannot have two points that share the same $x$ value. 
Your $x$ values are -9, -1, 2 and 7.  All your $x$ values are unique (i.e. no repetition), and thus we may conclude that this is indeed a function.
A: why not plot the 
points and see how how the graph looks
A: One way to precisely define a function is as follows: A function is a collection of ordered pairs, no two of which have the same first term. From this definition, it is immediate that your collection of ordered pairs is a function.
A: All first coordinates are distinct.  It's the graph of a function.
A: It is a function from the set $\{-9,-1,2,7\}$ into a set containing $\{-3,-1,7\}$. As long as each element of the domain, $\{-9,-1,2,7\}$, gets mapped unambiguously to a value (not necessarily distinct), this is a well-defined function.
A: You only think it fails the vertical line test at $x=1$ because you drew the graph incorrectly. 
You plotted the points you were given, but you also plotted many points that you were not given. You drew a bunch of lines, but there was nothing in the question about lines.  The correct graph has four isolated points—the four that were given to you—with nothing in between. Your graph includes points at $(1,1)$ and $(1,-\frac{13}{11})$. But there is nothing in the definition of this function that says it has any values at $x=1$. 
A: The domain of your function is just 4 discrete numbers. What you do when you draw lines between them is extend the domain to the interval [-9, 7], where every point between the interval's limits would be a member of the set. Like 5, but also 1.25, $\sqrt{2}$ and $\pi$.
BTW, notice that connecting the dots does result in a function, if you first order your set:  
$$\{(−9,−3),(−1,−1),(2,−1),(7,7)\}$$  
and that can't be right; the set {−9, 2, 7, −1} is the same as {−9, -1, 2, 7}.
A: As long as every point of domain is related to exactly one point of co-domain(vice versa need not be true),that relation is a function.Two or more points of domain can be related to a single point in co-domain. 
you can remember it like this:
One can have exactly one father, but a father can have one or more children.
Here child is a point of domain and father, a point of co-domain.
In the given problem, each point of domain has a unique image and hence it is a function.
A: It is a function, because every value in the domain has one value in the codomain. You may be confused because you are plotting the points and linking them with lines in the order they are given.
A simple test: are there two $y$ values that have the same $x$ value? If the answer is yes, then the relation is not a function; if the answer is no, then the relation IS a function.
