Math Problem Statement
Solution
The problem asks you to graph the equation and find the corresponding -values for the given -values: .
Step-by-Step Solution:
-
Understand the Equation: The equation involves the absolute value function , which always returns a non-negative value. The term shifts the graph downward by 2 units.
-
Calculate -values:
- For :
- For :
- For :
- For :
- For :
- For :
- For :
Completed Table:
-3 | 1 |
-2 | 0 |
-1 | -1 |
0 | -2 |
1 | -1 |
2 | 0 |
3 | 1 |
Now you can plot these points on the graph to represent the function .
Would you like any further details or have any questions?
Here are some related questions to deepen your understanding:
- How does the graph of compare to the graph of ?
- What effect does adding or subtracting a constant from have on its graph?
- How would the graph change if the equation was ?
- What are the key features of the graph of an absolute value function?
- Can you generalize the shape of for any constant ?
Tip: Remember that the absolute value function is V-shaped and symmetrical about the y-axis. Adjusting it vertically shifts the entire graph up or down.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Function
Graphing Linear Equations
Formulas
y = |x| - 2
Theorems
Absolute Value Properties
Suitable Grade Level
Grades 6-8