To find the limit of $g(x)$ as $x$ approaches 8 from the right (denoted $\lim_{x \to 8^+} g(x)$), we need to analyze the behavior of the function values as $x$ gets closer to 8 from values greater than 8.

The given table shows the following values:

• For $x = 8.025$, $g(x) = -5.2$
• For $x = 8.005$, $g(x) = -5.04$
• For $x = 8.001$, $g(x) = -5.008$
• For $x = 8$, $g(x) = 8$
• For $x = 7.999$, $g(x) = 0.008$
• For $x = 7.995$, $g(x) = 0.04$
• For $x = 7.975$, $g(x) = 0.2$

From this data, we observe that as $x$ approaches 8 from the right, the values of $g(x)$ move toward 0. Therefore, the reasonable estimate for $\lim_{x \to 8^+} g(x)$ is 0.

Thus, the correct answer is: B) 0

Would you like more details or have any questions? Here are some related questions:

1. What does the notation $\lim_{x \to 8^+} g(x)$ mean in terms of a one-sided limit?
2. How would you approach finding limits for other functions from tables of values?
3. What is the difference between $\lim_{x \to 8^+} g(x)$ and $\lim_{x \to 8^-} g(x)$?
4. How can you estimate limits when the table gives values for $g(x)$ as $x$ approaches a value from both directions?
5. What does it mean for a limit to "not exist"?

Tip: When estimating limits from a table, focus on the values of $g(x)$ as $x$ approaches the limit point from both sides. If the function values converge to the same value, that is the limit.