Question

the graph of the function f is shown above. what is $limlimits_{x \to 2^+} f(x)$?
a 1
b 3
c 4
d nonexistent

Explanation:

Step1: Recall the definition of a limit as \( x \) approaches a value from the right (right-hand limit). The right-hand limit \( \lim_{x \to a^+} f(x) \) is the value that \( f(x) \) approaches as \( x \) gets closer to \( a \) from values greater than \( a \).

Step2: Analyze the graph for \( x \to 2^+ \) (approaching \( x = 2 \) from the right side). From the graph, as \( x \) approaches 2 from values greater than 2 (moving along the graph towards \( x = 2 \) from the right), the function \( f(x) \) approaches the value 4. So, \( \lim_{x \to 2^+} f(x)=4 \).

Answer:

C. 4