# lim x-->-1- f(x) = ?

Jan 14, 2017

The answer to all a,b,c,d, is $1$.

#### Explanation:

All we care about is what happens at, or near

$x = - 1$

$f$ is constant (its value doesn't change) near $x = - 1$
No matter if we approach $- 1$ from the left or the right, $f$ remains constant at $f \left(x\right) = 1$

Since $f$ is also defined at that point, it holds that both one-sided limits (questions a,b) exist, are real numbers, and equal to $1$, so the general limit (two sided limit, question c) also exists and is $1$. Finally, judging from the graph, $f \left(- 1\right)$ is clearly defined, and equal to $1$ (question d).