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!