Examples of wavy functions needed

Question

There are many functions, the graphs of which appear as waves on X-axis of Cartesian plane, with ever increasing amplitude as $x$ approaches $–\infty$. eg. $y=x^n \sin(x)\cos(x)$ Can you provide me with some more examples of such functions?

Answer 1

Functions like$$e^{kx} \sin bx$$ and $$e^{kx} \cos bx$$ with different values of $k$ and $b$ are other examples of wavy functions.

Answer 2

Some examples:

1. $\frac12(e^x + e^{-x}) \sin x$

2. $|x| \sin x$

3. $\ln|x| \sin x$

4. $\sqrt{1+x^2} \sin x$

5. $e^{e^x+e^{-x}} \sin x$