Questions: The graph below is the function f(x) Find lim x → 2- f(x) Find lim x → 2+ f(x) Find lim x → 2 f(x) Find f(2)

Transcript text: The graph below is the function $f(x)$ Find $\lim _{x \rightarrow 2^{-}} f(x)$ $\square$ Find $\lim _{x \rightarrow 2^{+}} f(x)$ $\square$ Find $\lim _{x \rightarrow 2} f(x)$ $\square$ Find $f(2)$ $\square$

Solution

Solution Steps

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

To find $\lim_{{x \to 2^-}} f(x)$, observe the value that $f(x)$ approaches as $x$ approaches 2 from the left. From the graph, as $x$ approaches 2 from the left, $f(x)$ approaches -2.

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

To find $\lim_{{x \to 2^+}} f(x)$, observe the value that $f(x)$ approaches as $x$ approaches 2 from the right. From the graph, as $x$ approaches 2 from the right, $f(x)$ approaches 1.

Step 3: Determine the limit as x approaches 2

To find $\lim_{{x \to 2}} f(x)$, check if the left-hand limit and the right-hand limit are equal. Since $\lim_{{x \to 2^-}} f(x) = -2$ and $\lim_{{x \to 2^+}} f(x) = 1$, the limit does not exist because the left-hand limit and the right-hand limit are not equal.