I think my intuition of the Laplace transform and transfer functions is broken.
Suppose I have a linear function which relates two quantities r to x as such:
$$ r(x) = -100x + 25 $$
i.e. a straight line off center with nothing to do with time.
If I want a transfer function of the form $ \frac{R(s)}{X(s)} $, what should I do?
I'm expecting a constant (or DC gain), because this has nothing to do with time.
For example, $r(1) = -100 + 25 = -75$
If $\frac{R(s)}{X(s)} = c$, how could I get a value of 75 if I input a step function $ X(s) = \frac{1}{s}$?