## Functions
$$f:\operatorname{dom}(f) \rightarrow \mathbb{R},\quad f(x)=\dots$$
- function - one $y$ (image) value per $x$ (preimage)
-- 1:1 function - unique $y$ for each $x$
+- 1:1 function - unique $y$ for each $x$ ($\sin x$ is not 1:1, $x^3$ is)
**Domain $\operatorname{dom}(f)$:** set of all $x$ values in function
- maximal (implied) domain - largest domain for which the rule is defined