In the formal definition of limits, $\lim_{x\to a}f\left(x\right)=L$ ,$f\left(x\right)$  stands for _________.

In the formal definition of limits, $\lim_{x\to a}f\left(x\right)=L$ ,$a$ stands for _________.

True or False: If the left-hand limit of a function exists then the limit of $f\left(x\right)$  exists. 

True or False: If the right-hand limit of a function exists then the limit of $f\left(x\right)$ exists.