Questions: The graph below is the function f(x) Find lim x→-1⁻ f(x)= □ Find lim x→-1⁺ f(x)= □ Find lim x→-1 f(x)= □ Find f(-1)= □

Transcript text: The graph below is the function $f(x)$ Find $\lim _{x \rightarrow-1^{-}} f(x)=$ $\square$ Find $\lim _{x \rightarrow-1^{+}} f(x)=$ $\square$ Find $\lim _{x \rightarrow-1} f(x)=$ $\square$ Find $f(-1)=$ $\square$

Solution

Solution Steps

Step 1: Determine the left-hand limit as x approaches -1

To find the left-hand limit of $ f(x) $ as $ x $ approaches -1, observe the value that $ f(x) $ approaches from the left side of -1. From the graph, as $ x $ approaches -1 from the left, $ f(x) $ approaches -3.

\[ \lim_{{x \to -1^-}} f(x) = -3 \]

Step 2: Determine the right-hand limit as x approaches -1

To find the right-hand limit of $ f(x) $ as $ x $ approaches -1, observe the value that $ f(x) $ approaches from the right side of -1. From the graph, as $ x $ approaches -1 from the right, $ f(x) $ approaches 2.

\[ \lim_{{x \to -1^+}} f(x) = 2 \]

Step 3: Determine the limit as x approaches -1

The limit of $ f(x) $ as $ x $ approaches -1 exists only if the left-hand limit and the right-hand limit are equal. Since the left-hand limit is -3 and the right-hand limit is 2, the limit does not exist.

\[ \lim_{{x \to -1}} f(x) \text{ does not exist} \]