To determine the limit $\lim_{x \to a} f(x)$ from a graph of the function $f$, follow these steps:

Steps to determine the limit from a graph:

1. Locate the point $x = a$ on the graph.
2. Examine the behavior of the function as $x$ approaches $a$ from both the left and the right side:
   • The left-hand limit is $\lim_{x \to a^-} f(x)$, which means the value of $f(x)$ as $x$ approaches $a$ from the left.
   • The right-hand limit is $\lim_{x \to a^+} f(x)$, which means the value of $f(x)$ as $x$ approaches $a$ from the right.
3. Determine if the left-hand limit and right-hand limit are equal:
   • If $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$, then the limit $\lim_{x \to a} f(x)$ exists, and its value is the common value of both one-sided limits.
   • If the left-hand and right-hand limits are not equal, then the limit $\lim_{x \to a} f(x)$ does not exist.
4. Special cases: If there is a hole, vertical asymptote, or jump at $x = a$, these will affect the existence of the limit.

You can upload the graph or describe it, and I’ll help you find the limit based on that.

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