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:
To complete the table, we need to evaluate for each value of by following these steps:
- Take the absolute value of .
- Apply a negative sign to the absolute value.
- Subtract 9 from the result.
Let's go through each case:
1. When :
2. When :
3. When :
4. When :
Now, we can complete the table:
-10 | -19 |
0 | -9 |
10 | -19 |
20 | -29 |
Would you like further details or have any questions?
Here are some related questions to explore:
- What would happen to if we added a positive constant instead of subtracting 9?
- How does the function behave for values of beyond those in the table?
- Can we express as a piecewise function based on 's value?
- How does compare to in terms of graph shape and position?
- What is the domain and range of ?
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