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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:

| \( x \)  | 8  | 10  | -11 | -15 |
|---------|----|-----|-----|-----|
| \( g(x) \) | -9 | -8  | -6  | -4  |

Would you like more details or have any further questions?

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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.

Complete the table below given that g(x) = f(-x). The table provides values for x and f(x), and the user is asked to fill in the corresponding values for g(x).

Solve a function transformation problem where g(x) = f(-x). Given values for f(x), find the corresponding values of g(x) using function reflection. Suitable for students in Grades 9-11.

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