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We are asked to find \(\lim_{x \to 0} \left( 2g(x) \right)\), based on the given graph of \(g(x)\).

### Steps:
1. **Evaluate \( \lim_{x \to 0} g(x) \)**: 
   - As \(x\) approaches 0 from both the left and right, the value of \(g(x)\) approaches 1, as indicated by the open circle at \(x = 0\) with \(g(0) = 1\).
   
2. **Apply the constant multiple rule for limits**:
   - Since \( \lim_{x \to 0} g(x) = 1 \), we can use the constant multiple rule to find:
   \[
   \lim_{x \to 0} \left( 2g(x) \right) = 2 \times \lim_{x \to 0} g(x) = 2 \times 1 = 2
   \]

Thus, the correct answer is **B) 2**.

Would you like further details or clarifications?

Here are 5 related questions:
1. What is the formal definition of a limit?
2. How do you compute limits for piecewise functions like \(g(x)\)?
3. What happens when a limit approaches a point of discontinuity?
4. How does multiplying by a constant affect the limit?
5. How can we graphically determine the limit of a function?

**Tip**: When working with limits, always check if the function behaves the same from both the left and right sides of the point!

Find lim_{x→0}(2g(x)), where g(x) is a piecewise function given graphically.

Learn how to solve the limit problem lim_{x→0}(2g(x)) using the graphical representation of g(x). This solution involves understanding the constant multiple rule for limits and two-sided limits. Suitable for students in Grades 11-12.

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