Question

evaluate the limit based on the graph of f shown. \\(\lim\limits_{x\to -3^-} f(x)\\) \\(-10,10\\) by \\(-10,10\\) \\(\lim\limits_{x\to -3^-} f(x)=\boxed{\infty}\\)

Explanation:

Step1: Understand Left-Hand Limit

The left - hand limit $\lim_{x
ightarrow - 3^{-}}f(x)$ means we look at the values of $f(x)$ as $x$ approaches - 3 from the left (values less than - 3).

Step2: Analyze the Graph

From the given graph, as $x$ approaches - 3 from the left side, the graph of the function $f(x)$ is moving upwards, which indicates that the function values are increasing without bound. In the context of limits, when a function's values increase without bound as $x$ approaches a certain value from a particular side, the limit is $+\infty$.

Answer:

$\lim_{x
ightarrow - 3^{-}}f(x)=\infty$ (or $+\infty$)