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Let's solve the function table for \( f(a) = -9|a| \).

### Step-by-step:
The function is defined as \( f(a) = -9|a| \), which means that for each value of \( a \), you will take the absolute value of \( a \) and then multiply it by -9.

#### Values of \( a \) given:
- \( a = -4 \)
- \( a = -2 \)
- \( a = 0 \)
- \( a = 2 \)

#### Now, calculate \( f(a) \) for each \( a \):

1. **For \( a = -4 \):**
   - \( |a| = |-4| = 4 \)
   - \( f(a) = -9 \times 4 = -36 \)

2. **For \( a = -2 \):**
   - \( |a| = |-2| = 2 \)
   - \( f(a) = -9 \times 2 = -18 \)

3. **For \( a = 0 \):**
   - \( |a| = |0| = 0 \)
   - \( f(a) = -9 \times 0 = 0 \)

4. **For \( a = 2 \):**
   - \( |a| = |2| = 2 \)
   - \( f(a) = -9 \times 2 = -18 \)

### Final Table:
\[
\begin{array}{|c|c|}
\hline
a & f(a) \\
\hline
-4 & -36 \\
-2 & -18 \\
0  & 0 \\
2  & -18 \\
\hline
\end{array}
\]

Do you have any questions or want more details? Here are five related questions to expand your understanding:

1. How does the absolute value affect negative inputs in a function?
2. What happens when you multiply absolute values by negative numbers?
3. Can you describe how the function would behave for positive and negative values of \( a \)?
4. How would the function change if the coefficient (-9) were positive?
5. What would happen if you changed the function to \( f(a) = -9a \) without the absolute value?

**Tip:** Remember, the absolute value of any number is always non-negative, so it turns negative numbers into positive ones before applying the rest of the function!

Complete the function table for f(a) = -9|a| with values a = -4, -2, 0, 2.

Learn how to complete a function table for f(a) = -9|a| by evaluating the function at different values of a. This example uses absolute value and negative multipliers, suitable for students in Grades 8-10.

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