Questions: Use the graph of the function f shown to estimate the following limits and the function value. Complete parts (A) through (D). (A) Find lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x -> 2^- A. lim x -> 2^- f(x)=□ (Type an integer.) □ B. The limit does not exist. (B) Find lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x -> 2^+ A. lim x -> 2^+ f(x)=□ (Type an integer.)

Solution Steps

We are looking for the value that $f(x)$ approaches as $x$ approaches 2 from the left ($x \rightarrow 2^{-}$). Tracing the graph from the left, we see the function is a horizontal line at $y=-1$ until an open circle at $x=2$. The value of the function approaches $-1$ as $x$ approaches 2 from the left.

We are looking for the value that $f(x)$ approaches as $x$ approaches 2 from the right ($x \rightarrow 2^{+}$). Tracing the graph from the right, we see the function value is 2 when $x$ is slightly greater than 2. As $x$ approaches 2 from the right, the value of the function approaches 2.

(A) $\lim _{x \rightarrow 2^{-}} f(x)= -1$. So the answer is A, \(\boxed{-1}\).

(B) $\lim _{x \rightarrow 2^{+}} f(x) = 2$. So the answer is A, \(\boxed{2}\).

Final Answer