$A=\{1,2,3,4,5\}$, $B=\{1,2\}$ How many functions $f:A\rightarrow B$ exists

$A=\{1,2,3,4,5\}$, $B=\{1,2\}$ How many functions $f:A\rightarrow B$ exists

pI`m trying to calculate how much functions there is forbr
$A=\{1,2,3,4,5\}$, $B=\{1,2\}$ that $f:A\rightarrow B$br I know that
$f(a_{i})=y\in B $ and only one from A, but there is two option the first
that all goes to $1\in B$ and the second that all goes to $2\in B$ so its
$5$ for the first and $5$ for the second, how should I continue from
here?br br another related question that I have is how many functions
exists ($f:A\rightarrow A$) Injective and Surjective have on $A=\{1,2,
\dots ,n\}$? br thanks!/p