Question

evaluate the limit based on the graph of f shown. \\(\lim\limits_{x\to -4^{-}} f(x)\\) \\(\lim\limits_{x\to -4^{-}} f(x)=\square\\) - 10,10 by - 10,10

Explanation:

Step1: Understand the left - hand limit

The limit \(\lim_{x
ightarrow - 4^{-}}f(x)\) represents the value that \(f(x)\) approaches as \(x\) gets closer to \(-4\) from the left - hand side (values of \(x\) that are less than \(-4\) but very close to \(-4\)).

Step2: Analyze the graph

From the given graph, when we look at the behavior of the function \(f(x)\) as \(x\) approaches \(-4\) from the left (moving along the \(x\) - axis towards \(-4\) from values less than \(-4\)), we observe the \(y\) - value that the graph is approaching. The horizontal line (or the part of the graph) for \(x
ightarrow - 4^{-}\) seems to approach \(0\) (since the graph is on the horizontal axis, which has a \(y\) - value of \(0\) for that part when approaching from the left of \(-4\)).

Answer:

\(0\)