use the graph of f(x) to find the limit. lim f(x) = x→2

Explanation:

Step1: Observe left - hand limit

As $x$ approaches 2 from the left side ($x\to2^{-}$), we look at the values of the function on the graph. Following the curve as $x$ gets closer to 2 from the left, $f(x)$ approaches 7.

Step2: Observe right - hand limit

As $x$ approaches 2 from the right side ($x\to2^{+}$), we follow the curve. As $x$ gets closer to 2 from the right, $f(x)$ approaches 7.

Step3: Determine the limit

Since the left - hand limit $\lim_{x\to2^{-}}f(x)$ and the right - hand limit $\lim_{x\to2^{+}}f(x)$ are both equal to 7, the limit $\lim_{x\to2}f(x)=7$.

Answer:

7