Is an identity function one – one function?

All one-one functions are onto functions.

There will be no one-one function from $A$ to $B$ when $n\left(A\right)=4$ and $n\left(B\right)=3$.

There will be no onto function from $A$ to $B$ when $n\left(A\right)=4, n\left(B\right)=5$.

If $f$ is a bijection from $A$ to $B$, then $n\left(A\right)=n\left(B\right)$.

If $n\left(A\right)=n\left(B\right)$, then $f$ is a bijection from $A$ to $B$.

All constant functions are bijections. 

Determine whether the graph given below represent a function. Give reason for your answer.