Functions with subscripts? In the equation:
$f_\theta(x)=\theta_1x$
Is there a reason that $\theta$ might be a subscript of $f$ and not either a second parameter or left out of the left side of the equation altogether? Does it differ from the following?
$f(x,\theta)=\theta_1x$
(I've been following the Machine Learning class and the instructor uses this notation that I've not seen before)

I personally dislike the notation. And I believe it means different things in different contexts. For example, it means the opposite of what the other answers say in probability, see:
https://en.wikipedia.org/wiki/Likelihood_function#Discrete_probability_distribution
It is shown that $P_{\theta}(X = x)$ and $p_{\theta}(x)$ both mean that $X/x$ is the constant variable in this context and we are plotting with respect to $\theta$.
