A limit is the value that the function approach as x approaches "a".

In the given problem, the `x-gt-` `oo` indicates that independent variable x approaches large negative numbers for given function:` f(x)=tanh(x)` .

The function `f(x)= tanh(x)` is the **hyperbolic tangent function**. Its domain is all real number that can be expressed with the interval notation` (-oo,oo)` . It is a symmetric odd function. It also has an inflection point that can be found at x=0. There are no local extrema that can found in the continuous function of hyperbolic tangent.

The "attached image" is the graph of `f(x)=tanh(x)` .

By graphical inspection, as graph continues to left of y-axis or x approaches `-oo` , it approaches `y = -1` .

Therefore, the limit will be:

`lim_(x-gt-oo) [tanh(x)] = -1` .