intuitively, a function is periodic if it has a repeating pattern, forever. sin(x) is obviously one. it's period is . you have the same pattern between repeating forever.
slightly more formally, a function is called periodic, if for some integer . we call the period.
for example, going back to sine. , the period is . any multiple of the period and you get back the same value. so etc
a function is called one-to-one if . or equivalently, for