could someone please explain me how to find if something is a injection, surjection, and a bijection with some good examples

Question

anonymous · Answer

Answers.com always give great examples & work sheet practices /help websites

anonymous · Answer

Injection: For all $x \in X$, there exists $y \in Y$ such that $f(x)=y.$
Surjection: For all $y \in Y$, there exists at least one $x \in X$ such that $y=f(x).$
Bijection: Injection+Surjection

Do you follow so far?

anonymous · Answer

yeahh i have the definition but just wanted to back it up with good exampless

anonymous · Answer

$$\begin{align}
X&=\{1,2\}\
Y&=\{2,4,6\}\
f: X &\to Y\
x &\mapsto 2x
\end{align}$$
What do you think $f$ is?

anonymous · Answer

$$
\begin{align}
X&=\{0,1\}\
Y&=\{-1,0\}\
g: X&\to Y\
x &\mapsto x-1
\end{align}
$$
What do you think $g$ is?

anonymous · Answer

$$
\begin{align}
X&=\{-4,-2,0,2,4\}\
Y&=\{0,4,16\}\
h:X &\to Y\
x &\mapsto x^2
\end{align}
$$
What do you think $h$ is?