Use the graph of the given function f to determine 
lim 
x→a 
f(x)
 at the indicated value of a, if it exists.

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.

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Use the graph of the given function f to determine lim x→a f(x) at the indicated value of a, if it exists.

Learn how to determine the limit of a function as x approaches a specific value using a graph. This explanation covers the concept of left-hand and right-hand limits, graphical behavior, and limit existence criteria. Suitable for high school students in Grades 10-12.

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