question 27 the graph below is the function f(x) find lim f(x) x→ - 1 - find lim f(x) x→ - 1 + find lim f(x)…

Explanation:

Step1: Analyze left - hand limit

As (x\to - 1^{-}), we look at the values of the function as (x) approaches (-1) from the left side of the graph. Following the part of the graph for (x < - 1), we see that the (y) - value approaches (1). So, (\lim_{x\to - 1^{-}}f(x)=1).

Step2: Analyze right - hand limit

As (x\to - 1^{+}), we look at the values of the function as (x) approaches (-1) from the right side of the graph. Following the part of the graph for (x>-1), we see that the (y) - value approaches (2). So, (\lim_{x\to - 1^{+}}f(x)=2).

Step3: Analyze overall limit

Since (\lim_{x\to - 1^{-}}f(x)=1) and (\lim_{x\to - 1^{+}}f(x)=2), and (1\neq2), (\lim_{x\to - 1}f(x)) does not exist (DNE).

Step4: Find function value

The solid dot on the graph at (x = - 1) has a (y) - value of (-3). So, (f(-1)=-3).

Answer:

(\lim_{x\to - 1^{-}}f(x)=1) (\lim_{x\to - 1^{+}}f(x)=2) (\lim_{x\to - 1}f(x)) DNE (f(-1)=-3)