I need a head check on this one. Suppose $\sigma,\mu \in \mathbb{R}$ and $\sigma \neq 0$. Let $X$ be a random variable with density $f_X(x)$. I think that the random variable $Z:= \sigma X + \mu$ has density $ f_Z(x) = \frac{1}{|\sigma|}f_X\left(\frac{x-\mu}{\sigma} \right). $
Splitting the cases $\sigma > 0$ and $\sigma<0$ my proof comes down to a simple change of variables. However, I can't find any mention of a formula like this on wikipedia or google. Is it so simple that no one thought to mention it, or am I misunderstanding?