Talk:Graph of a function

I don't think this is a very clear explanation of graphing polynomials. I think the general idea of a graph should be shown instead; explaining what a graph is (representation of f(x) vs. x), instead of having a tutorial of graphing polynomials, since the graphs drawn by these tutorials won't be really accurate anyways. What does everyone else think? Myself 01:23, 13 August 2006 (EDT)

Reply

How would you draw more accurate graphs? How accurate do the graphs need to be? What is the purpose of drawing a graph? Certainly we can't use graphs as evidence in a rigorous proof. Graphs provide a visual way to look at functions and allow for conjectures about them as one use, right? I don't see why we should take out the tutorial on graphing. Certainly please add any additional info you think is pertinent (like f(x) vs. x).

I just don't see how useful knowing what a graph is if you can't draw one. --Joe 11:07, 13 August 2006 (EDT)

To clarify, what I was saying is that the graphs are not accurate because they are not graphs, they are approximations. Take a look at the 2nd "graph". It says,

Likewise, a sign analysis on the intervals (-3/2,1) and (1,∞) allows the graph to be drawn as a smooth curve curve through the zeros using this information as a guideline

Notice how this does not mention anything about drawing a graph but only describes a way to approximate one. With an actual graph, you can get the value of each point, but with these, you get different values depending on what you draw.Myself 19:41, 13 August 2006 (EDT)

So how we draw a true graph? Plot every single point? Just tell them to plug it in their calculator? Even then, the calculator only outputs an approximate. The question is how accurate do people need to be able to draw graphs by hand?

We could teach how to make more accurate graphs of polynomials using calculus, but that's beyond the scope of this article (this can go somewhere else or we can add on to this article).

I'm saying add additional information about the idea of a graph at the beginning but leave the rest as it is. What are you suggesting? -- Joe 23:44, 13 August 2006 (EDT)

Using we in mathematical writing

It's ok to use the first person "we" in mathematical writing (this isn't english class :P ). Here are some references: here and here. You can just leave the page how it is for now. --Joe 11:27, 13 August 2006 (EDT)

Of course it's okay to use "we" in mathematical writing, but I thought the AoPS wiki was for definition/guides to problem solving and problem solving topics? Perhaps I am being too picky, or am reading too much Wikipedia.Myself 19:44, 13 August 2006 (EDT)