What is the equation of a curve like this (constant then an inflection then straight again)? Thanks in advance.
If you want the function to be smooth then one which approximates the shape you drew is a sigmoid:
$\displaystyle
f(x) = \frac{1}{1+e^{-x}}
$
This function has a range of (0,1) but is not constant anywhere (though you can tighten up the function to make the derivative very small as x goes away from 0)
You can also define such a function peicewise if you want the function to be constant on some intervals.
Shifting a function up (or down) by a fixed amount can be done by adding (or subtracting) a constant from the function. The sigmoid function is already above the x=0 line in the plane since
$\displaystyle
x \rightarrow \infty,
f(x) \rightarrow 1
$
while
$\displaystyle
x \rightarrow -\infty,
f(x) \rightarrow 0
$
To shift a function left (or right) change the input by a constant.
exp:
f(x) shifted to the right by 5 is f(x-5)
f(x) shifted to the left by 5 is f(x+5).