Messing around with a graphing calculator, I noticed that after I raised $f(x) = x$ to some large negative number, the two vertical lines stretching from $-1$ and $1$ stopped. I have a few questions:
How do I find out at exactly what point this happens?
Why does this happen?
Is it just a rounding error or something in the graphing calculator that makes this occur?
I would appreciate any answers or leads.
It happens when k tends to infinity, just look at the chart of an exponential function. If the base is more then one then it tends to 0 for x that tends to minus infinity. Else if the base is less then one then it tends to infinity.
Maybe it is more clear like this: $$a > 1 \to \lim_{x\to -\infty} a^x = 0$$ $$a < 1 \to \lim_{x\to -\infty} a^x = \infty$$ While: $$\lim_{x\to -\infty} 1^x = 1$$
This is also the interpretation of the chart.
Exactly.. look for example at the following pictures (they are taken from google online chart, just type your function on google search bar).
plot of f(x) = x^(0-1000000)
Just by zooming a bit:
you see that it is an approximation.