To find the limit $\lim_{x \to 0} (g(x) - h(x))$, let's analyze both functions $g(x)$ and $h(x)$ as $x$ approaches 0.

Step 1: Evaluate $g(x)$ as $x \to 0$

From the graph of $g(x)$, we observe that as $x$ approaches 0 from both the left and the right:

• $g(x)$ approaches 1 from both sides.

Thus, $\lim_{x \to 0} g(x) = 1$.

Step 2: Evaluate $h(x)$ as $x \to 0$

From the graph of $h(x)$, we observe that as $x$ approaches 0 from both the left and the right:

• $h(x)$ approaches 1 from both sides.

Thus, $\lim_{x \to 0} h(x) = 1$.

Step 3: Compute $\lim_{x \to 0} (g(x) - h(x))$

Now, subtract the limits we calculated: $\lim_{x \to 0} (g(x) - h(x)) = \lim_{x \to 0} g(x) - \lim_{x \to 0} h(x) = 1 - 1 = 0$

Conclusion:

The limit is 0, so the correct answer is B. 0.

Would you like more details or have any questions?

Here are some related questions you might find helpful:

1. What happens if one of the functions is discontinuous at $x = 0$?
2. How do you approach limits when graphs have vertical asymptotes?
3. What is the formal definition of a limit from the left and the right?
4. How do piecewise functions affect the computation of limits?
5. What happens to the limit if $g(x)$ or $h(x)$ is undefined at $x = 0$?

Tip: When analyzing limits graphically, always check the behavior from both sides of the point of interest!