Complete the table.

f(w) = 8|w| − 5
w	f(w)
–9	
–8	
–7	
–6	



To complete the table, we will use the function \( f(w) = 8|w| - 5 \). The absolute value of \( w \) ensures that the output of \( |w| \) is always positive.

Now, let's calculate \( f(w) \) for each value of \( w \):

1. For \( w = -9 \):
   \[
   f(-9) = 8|{-9}| - 5 = 8 \times 9 - 5 = 72 - 5 = 67
   \]

2. For \( w = -8 \):
   \[
   f(-8) = 8|{-8}| - 5 = 8 \times 8 - 5 = 64 - 5 = 59
   \]

3. For \( w = -7 \):
   \[
   f(-7) = 8|{-7}| - 5 = 8 \times 7 - 5 = 56 - 5 = 51
   \]

4. For \( w = -6 \):
   \[
   f(-6) = 8|{-6}| - 5 = 8 \times 6 - 5 = 48 - 5 = 43
   \]

Now, we can complete the table:

\[
\begin{array}{|c|c|}
\hline
w & f(w) \\
\hline
-9 & 67 \\
-8 & 59 \\
-7 & 51 \\
-6 & 43 \\
\hline
\end{array}
\]

Would you like further details on how the function works or any of the steps? 

Here are some related questions you might find useful:
1. What is the significance of the absolute value in the function?
2. How would the function change if the constant term was different?
3. How would the function behave for positive values of \( w \)?
4. What would happen if the coefficient of \( |w| \) was not 8?
5. Can you graph this function for values of \( w \) from -10 to 10?

**Tip**: The absolute value function ensures symmetry, so \( f(w) = f(-w) \).

Complete the table.
f(w) = 8|w| − 5
w    f(w)
–9    
–8    
–7    
–6    

Learn how to complete the table using the function f(w) = 8|w| - 5. This problem covers algebraic concepts such as absolute value and linear functions, suitable for students in Grades 7-9. The table is filled with values calculated step-by-step for w = -9, -8, -7, and -6.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation