Question

13 mark for review the graph of the function f is shown. what is lim f(x) ? x→2

Explanation:

Step1: Analyze left - hand limit

As $x$ approaches $2$ from the left side ($x\to2^{-}$), we observe the values of $y = f(x)$ on the graph. The function values approach $3$.

Step2: Analyze right - hand limit

As $x$ approaches $2$ from the right side ($x\to2^{+}$), the function values also approach $3$ on the graph.

Step3: Determine the limit

Since the left - hand limit $\lim_{x\to2^{-}}f(x)=3$ and the right - hand limit $\lim_{x\to2^{+}}f(x)=3$, then $\lim_{x\to2}f(x)=3$.

Answer:

$3$