Question

use the given graph of f to state the value of each quantity, if it exists. (if an answer does not exist, enter dne.) (a) $limlimits_{x \to 2^-} f(x)$
4 ×
(b) $limlimits_{x \to 2^+} f(x)$
0 ×
(c) $limlimits_{x \to 2} f(x)$
dne ✔ great work.
(d) $f(2)$
3 ✔ fantastic!
(e) $limlimits_{x \to 4} f(x)$
4 ✔ good!
(f) $f(4)$
dne ✔ fantastic!

Explanation:

Part (a)

Step1: Understand left - hand limit

The left - hand limit as \(x
ightarrow2^{-}\), denoted as \(\lim_{x
ightarrow2^{-}}f(x)\), is the value that \(f(x)\) approaches as \(x\) gets closer to \(2\) from the left - hand side (values of \(x\) less than \(2\)).

Step2: Analyze the graph

Looking at the graph, as \(x\) approaches \(2\) from the left (the part of the graph before \(x = 2\) on the left - hand side), the \(y\) - value that the graph approaches is \(3\). So \(\lim_{x
ightarrow2^{-}}f(x)=3\).

Part (b)

Step1: Understand right - hand limit

The right - hand limit as \(x
ightarrow2^{+}\), denoted as \(\lim_{x
ightarrow2^{+}}f(x)\), is the value that \(f(x)\) approaches as \(x\) gets closer to \(2\) from the right - hand side (values of \(x\) greater than \(2\)).

Step2: Analyze the graph

Looking at the graph, as \(x\) approaches \(2\) from the right (the part of the graph after \(x = 2\) on the right - hand side), the \(y\) - value that the graph approaches is \(1\). So \(\lim_{x
ightarrow2^{+}}f(x)=1\).

Answer:

3