“Is” is a very overworked word, to the point of illogicality.
Technically in both cases none of them.
In everyday language we can get away with the question and accept the answer “The first one” even though it is actually a picture of the head of a dog.
In math we MUST be more precise, and ask “Which of these graphs is the graph of a function?”, or “Which of these graphs could represent a function?”.
A graph is NEVER a function, and a function is not a graph. If we actually followed the Common Core on this it would be even more troublesome, as a graph is DEFINED as a set of ordered pairs as below —
…………………………………………
Functions 8.F
Define, evaluate, and compare functions.
1. Understand that a function is a rule that assigns to each input exactly
one output. The graph of a function is the set of ordered pairs
consisting of an input and the corresponding output.
…………………………………………
But at least WE all know what a graph is…..or do we?
Saving school math 
Hmm.. I suck at math.. I do writing. but Common Cores Standard seems fairly easy to understand, an d seems to agree with everyone else’s .. what am I missing?
A function f is even if its graph is symmetric with respect to the y-axis. This criterion can be stated algebraically as follows: f is even if f(-x) = f(x) for all x in the domain of f. For example, if you evaluate f at 3 and at -3, then you will get the same value if f is even.
Graphs of Functions
dl.uncw.edu/digilib/mathematics/algebra/…/functions/graphs/graphs.html
Graph of a function – Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Graph_of_a_function
Wikipedia
In mathematics, the graph of a function f is the collection of all ordered pairs (x, f(x)). If the function input x is a scalar, the graph is a two-dimensional graph, and …
Graphs of Functions
dl.uncw.edu/digilib/mathematics/algebra/…/functions/graphs/graphs.html
A function f is even if its graph is symmetric with respect to the y-axis. This criterion can be stated algebraically as follows: f is even if f(-x) = f(x) for all x in the domain of f. For example, if you evaluate f at 3 and at -3, then you will get the same value if f is even.
Just a thought.. after reading your bio you should go over to OERCommons or KhanAcademy or maybe Betterlesson and put together a few CommonCore Lessons. That way you can put a voice in where it might be heard by those who can do something about what you discovered needs repair. See, with CommonCore, came OpenEducation.. The best known project is EngageNY, which a lot of schools are using now.
OpenEdu is peer reviewed (you could do some serious help in that area), designed by some of the best minds, and liquid, meaning that if you did find something wrong, it is changed and everyone updates the same day.None of this stuff about waiting a year or having to explain why the class is learning the wrong stuff. If you discovered something wrong with the CCSS itself, they would welcome your voice. Seriously, they would.
I think he was simply saying that the language used is inaccurate. But I don’t think this is pedantic, since in mathematics everything rests on definitions. Obviously, the graph is a visual representation of the function. The entire domain and range of the function may not fit on the graph you are viewing, so in a way this would be comparable to calling the picture of the head of a dog a picture of a dog. At least, that is what I believe he was getting at.
Actually, this is even funnier than that because the caption says “which of these is these heads is a dog” … which is pretty far from “which of these is the image of the head of a dog.” I think the analogy to functions and graphs is pretty spot on!