Answer:
The limit of the function as x approaches to -1, is -1 and the option 4 is correct.
Step-by-step explanation:
According the the definition of limit, if,
[tex]L=\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)[/tex]
Then the limit of function exist. Either the function is defined or not on the point a. If the at point a the value value of function is L, then the function is continuous.
From the given graph it is easily noticed that the value of f(x) approaches to -1 as x approaches to -1 from left or left. At x=-1 there is a open circle on (-1,-1), therefore this is not included in the function.
The value of f(x) is 2 at x=-1 because of the point (-1,-2).
[tex]\lim_{x\rightarrow -1^+}f(x)=\lim_{x\rightarrow -1^-}f(x)=-1[/tex]
Therefore the limit of the function exist and the limit of the function is -1.
