I am trying to generate some plots for certain function with certain properties. For example, $f$ is increasing from $a$ to $b$, with second derivative decreases exponentially, etc. (this is just a silly example). Please note that this is not about plotting a specific function but rather obtaining certain shapes.
Is there a program to help me generate plots without the need of a closed form of the function - just its properties?
The reason I ask this is because after proving some theorems with a general function $f(x)$ with certain properties, I want to show it graphically on my report.