JUST can anyone fucking explain this to me already I JUST dont

btw im talking about exponential functions as a whole

>>8020773
what is there to explain

they are functions

they grow fast or slow depending on numbers

>>8020781
desu they all grow pretty fast

File: tpb.jpg (14KB, 228x308px) Image search: [Google]

14KB, 228x308px

>>8020781
i know that but i lost all my memories about this school shit, so i tried to ask /sci because this seems like the easiest thing in the world for you neckbeards

>>8020792
Remember that raising a number to a negative power is the same as raising its reciprocal to the same power but negative, so all of those fractional functions can be rewritten as [math]2^{-x}[/math] etc.

So you're plotting the function [math]f(x)[/math] and [math]f(-x)[/math], which means it's going to be mirrored across the y-axis.

Meanwhile, [math](n+1)^x[/math] gets bigger more quickly than [math]n^x[/math] for positive values of [math]x[/math], but also gets smaller more quickly for negative values of [math]x[/math].

That's it.

>>8020789
1^x

>>8020773
What doesn't make sense to you in particular? You do know how exponentiation works, both the intuitive definition, as well as expansion of that onto negative, rational, and irrational exponents?

The exponential function is a good showcase of the flaws of the cartesian coordinate system. The graph of [math]e^x[/math] looks to us like almost all of it is either "almost flat" or "almost vertical", while in fact its slope is changing all the time.

What is misleading to us is that we tend to perceive "slope" as "angle of tangent", and that angle doesn't change linearly as slope does. Instead, it asymptotically approaches [math]\frac{\pi}{2}[/math] as slope approaches [math]\infty[/math]. While we can easily tell slopes such as [math]3[/math], [math]1[/math], and [math]\frac{1}{3}[/math] apart from one another, we cannot tell apart slope [math]50[/math] from slope [math]100000[/math] (or slope [math]\frac{1}{50}[/math] from slope [math]\frac{1}{100000}[/math]) anymore.

>>8020773
a^0 for a=/=0 is 1, what's not to get?

>>8020810
>>8020912
>>8020896
thanks !

>>8020912
It's really hard to help him for as long as he doesn't tell precisely what he is struggling to understand.

>>8020939
it's the only thing that stuck out