Math Problem Statement

Complete the table using the function f(c) = -|c| - 9 with given values of c (-10, 0, 10, 20).

Solution

The function given is:

f(c)=c9f(c) = -|c| - 9

To complete the table, we need to evaluate f(c)f(c) for each value of cc by following these steps:

  1. Take the absolute value of cc.
  2. Apply a negative sign to the absolute value.
  3. Subtract 9 from the result.

Let's go through each case:

1. When c=10c = -10:

f(10)=109=109=19f(-10) = -|-10| - 9 = -10 - 9 = -19

2. When c=0c = 0:

f(0)=09=09=9f(0) = -|0| - 9 = 0 - 9 = -9

3. When c=10c = 10:

f(10)=109=109=19f(10) = -|10| - 9 = -10 - 9 = -19

4. When c=20c = 20:

f(20)=209=209=29f(20) = -|20| - 9 = -20 - 9 = -29

Now, we can complete the table:

ccf(c)f(c)
-10-19
0-9
10-19
20-29

Would you like further details or have any questions?


Here are some related questions to explore:

  1. What would happen to f(c)f(c) if we added a positive constant instead of subtracting 9?
  2. How does the function f(c)=c9f(c) = -|c| - 9 behave for values of cc beyond those in the table?
  3. Can we express f(c)f(c) as a piecewise function based on cc's value?
  4. How does f(c)=c9f(c) = -|c| - 9 compare to g(c)=c9g(c) = |c| - 9 in terms of graph shape and position?
  5. What is the domain and range of f(c)=c9f(c) = -|c| - 9?

Tip: Absolute values always yield non-negative results, so applying a negative sign to them will always make them non-positive.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value
Function Evaluation

Formulas

f(c) = -|c| - 9

Theorems

-

Suitable Grade Level

Grades 6-8