Question

use the graph to find the indicated limits.

step 1 of 3: find \\(\lim_{x \to 2^-} f(x)\\).

Explanation:

Identify the target value and direction

We need to find the left-sided limit of \(f(x)\) as \(x\) approaches \(2\), denoted as \(\lim_{x \to 2^-} f(x)\). This means we observe the \(y\)-values of the graph as \(x\) approaches \(2\) from values strictly less than \(2\) (from the left).

Trace the graph from the left

Looking at the graph, for \(x < 2\), the function is represented by the lower curve. As we move along this curve from left to right towards \(x = 2\), the curve ends at a solid blue point at \(x = 2\).

Determine the corresponding y-value

At \(x = 2\), the solid dot on this lower branch is located at \(y = -2\). Therefore, as \(x\) approaches \(2\) from the left, the function values approach \(-2\).

Answer:

Step 1 of 3: Find <blank>\(\lim_{x \to 2^-} f(x) = -2\)</blank>.