6
votes
3answers
117 views

Is $x^x$ a polynomial, an exponential or both?

If $c$ is a constant, and $x$ is a variable, we'd say that $f(x) = x^c$ is a polynomial function of order $c$. Conversely, the function $f(x) = c^x$ would be called an exponential function. Is there ...
2
votes
5answers
413 views

Which is actually exponential?

I've heard the term "exponential" applied to two sorts of functions: $$n^x\text{, where $n$ is a constant (e.g., $2^x$)}$$ and $$x^2$$ Which is really exponential, and what do I call the other ...
2
votes
1answer
75 views

Is there a name for the function $(1 - e^{ct})/(1 - e^{c})$?

$$f(t) = \frac{1 - e^{ct}}{1 - e^{c}}$$ This is a function which is somehow a streched exponential which is zero at $t = 0$, and one at $t = 1$, where $c$ determines the curvature (with $c = 0$, it ...
0
votes
3answers
761 views

What is the name of the function $f(x)=\frac{1}{x}$?

I'm facing this function: $$f(x)=\frac{1}{x}$$ What I know is that the above equation is one of the simplest forms of "rational functions", where the numerator is $1$ and the denominator is $x$. Is ...
4
votes
2answers
160 views

What consitutes an exponential function?

I was recently having a discussion with someone, and we found that we could not agree on what an exponential function is, and thus we could not agree on what exponential growth is. Wikipedia claims ...