Question

Using the graph of f(x) below, find limit as x approaches negative 1 of f of x. (4 points)

Answer 1

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,

$L=\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)$

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).

$\lim_{x\rightarrow -1^+}f(x)=\lim_{x\rightarrow -1^-}f(x)=-1$

Therefore the limit of the function exist and the limit of the function is -1.