You used the if operator incorrectly. The format is
if( condition, what to do if True, what to do if False)
But you put another condition in the place of "what to do if false".
Here's an example: I want a function which is equal to $3x$ between $x=1$ and $x=4$, is equal to $x+8$ between $x=4$ and $x=5$, and is undefined otherwise. The code could be
if(x>5, ln(0), if(x>4, x+8, if(x>1, 3*x, ln(0) ) ) )
Here I'm using $\ln(0)$ with the hope that it will simply produce no output for the corresponding range, rather than halt the entire computation. Don't have the app (or iPad for that matter), so can't tell for sure.
The prod( command will take the product of elements of a list for you, which handles finite products $\prod\limits_{i=1}^n$ just fine, especially in conjunction with the seq( command. For example, if you want to compute $n!$ the roundabout way, you can take
prod(seq(I,I,1,N))
which is the calculator approach to writing $\prod\limits_{i=1}^n i$.
There's no way to handle infinite products except to the extent that you can approximate them with finite products.
(I'm not sure if the color version of the TI-84 can handle infinite sums with the Σ( command; I doubt it. But if it does then you can use that and logarithms to do infinite products.)
Best Answer
Well, you can have maps from $\mathbb R^1$ to $\mathbb R^2$; viceversa, and from $\mathbb R^1$ to $\mathbb R^1$. The graph of a function $f(x): X \rightarrow Y $ is the set {$(x,y): y=f(x)$} for some $x$, which is a subset of the Cartesian product $X \times Y$ . Then you need $X \times Y$ to be of dimension $3$ or lower, or you would need $4$ dimensions to do the graphing.