The problem asks to complete the table given that $g(x) = f(-x)$.

We already have the values of $x$ and $f(x)$, and we are asked to fill in the table for $g(x)$. The key here is that $g(x) = f(-x)$, which means that the value of $g(x)$ at some $x$ is the same as $f(x)$ at the corresponding negative $x$.

Steps to Solve:

1. For each value of $x$ in the bottom table, find the corresponding value of $-x$ and use the known value of $f(-x)$ from the top table to fill in $g(x)$.

Let's go through each step:

For $x = 8$:

• We need $g(8) = f(-8)$.
• From the table, $f(-8) = -9$.
• So, $g(8) = -9$.

For $x = 10$:

• We need $g(10) = f(-10)$.
• From the table, $f(-10) = -8$.
• So, $g(10) = -8$.

For $x = -11$:

• We need $g(-11) = f(11)$.
• From the table, $f(11) = -6$.
• So, $g(-11) = -6$.

For $x = -15$:

• We need $g(-15) = f(15)$.
• From the table, $f(15) = -4$.
• So, $g(-15) = -4$.

Final Table:

Would you like more details or have any further questions?

Here are 5 follow-up questions that expand on this topic:

1. What is the relationship between even and odd functions with respect to $f(-x)$?
2. How would the table change if $g(x) = -f(-x)$?
3. How can you graphically represent the transformation $g(x) = f(-x)$?
4. If $f(x)$ is a linear function, how does $g(x) = f(-x)$ affect its slope and intercepts?
5. How would you approach the problem if given a quadratic function instead of $f(x)$?

Tip: When dealing with function transformations like $f(-x)$, you are performing a reflection of the graph across the y-axis.