https://file.aiquickdraw.com/mathbot/file/17254133976548oavzyhg.jpg

The image you uploaded shows a blackboard with four functions and a table of values labeled \( X \) and \( F(X) \). The functions written on the board are:

1. \( f(x) = 6^x \)
2. \( f(x) = 5^x \)
3. \( f(x) = 6^{-x} \)
4. \( f(x) = 5^{-x} \)

There is also a table of values for \( X \) and \( F(X) \) with the following entries:

\[
\begin{array}{c|c}
X & F(X) \\
\hline
3 & \\
2 & \\
1 & \\
0 & \\
-1 & \\
-2 & \\
\end{array}
\]

It seems like the task is to fill in the table for \( F(X) \) based on the provided functions. If you'd like, I can help you calculate the values of \( F(X) \) for each function at the specified \( X \) values.

Would you like to proceed with that, or do you have any specific questions about the functions or table?

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**Relative Questions:**

1. How does the behavior of exponential functions differ when the base is greater than 1 versus between 0 and 1?
2. What effect does negating the exponent in an exponential function have on the graph of the function?
3. How would you describe the asymptotes of the functions \( f(x) = 6^x \) and \( f(x) = 6^{-x} \)?
4. Can you explain the process of constructing a table of values for any function, given specific \( X \) values?
5. How does the function \( f(x) = 5^x \) compare to \( f(x) = 6^x \) in terms of growth rate?

**Tip:** When working with exponential functions, it's essential to understand how the base and the sign of the exponent affect the function's growth or decay.

The query submitted by the user involves analyzing the functions f(x) = 6^x, f(x) = 5^x, f(x) = 6^{-x}, and f(x) = 5^{-x} and constructing a table of values for specific X values.

Learn how to evaluate and graph exponential functions such as f(x) = 6^x, f(x) = 5^x, f(x) = 6^{-x}, and f(x) = 5^{-x}. This guide includes constructing a table of values for given X values and exploring the growth and decay behaviors of these functions. Suitable for students in Grades 9-12.

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