"Imagine a graph in which the x-axis depicts number of interest compounds per year and the y-axis depicts dollars owed. Does this function have a limit?"
Do the units on this graph make sense $ x compounds / year ?
Does the derivation of this graph tell me anything?
I'm very confused as to what I'm supposed to understand from this. No further explanation was provided with this question. Thanks for the help!
Try pushing ahead and making the graph. Pick some arbitrary principal (say $\$1,000.00$) and some arbitrary interest rate (say $5\%$).
Have the $x$-axis be the number of compounding periods. $x=1$ means that the interest is paid once, at the end of the year; $x=2$ means that half the interest is paid after six months, the other half at the end. $x=365$ means the interest is paid daily, $x=730$ that it is paid twice daily.
On the $y$-axis, plot the total amount of interest paid, or the total deposit including interest, or something of that sort. See how it comes out.
Then do it again, with a different principal and interest rate, and see what you learn.