Math Problem Statement

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

Solution

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

Step-by-step:

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

Values of aa given:

  • a=4a = -4
  • a=2a = -2
  • a=0a = 0
  • a=2a = 2

Now, calculate f(a)f(a) for each aa:

  1. For a=4a = -4:

    • a=4=4|a| = |-4| = 4
    • f(a)=9×4=36f(a) = -9 \times 4 = -36
  2. For a=2a = -2:

    • a=2=2|a| = |-2| = 2
    • f(a)=9×2=18f(a) = -9 \times 2 = -18
  3. For a=0a = 0:

    • a=0=0|a| = |0| = 0
    • f(a)=9×0=0f(a) = -9 \times 0 = 0
  4. For a=2a = 2:

    • a=2=2|a| = |2| = 2
    • f(a)=9×2=18f(a) = -9 \times 2 = -18

Final Table:

\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!

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Functions
Algebra

Formulas

f(a) = -9|a|
|a| = absolute value of a

Theorems

Absolute value theorem
Function evaluation

Suitable Grade Level

Grades 8-10