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The problem asks you to graph the equation \( y = |x| - 2 \) and find the corresponding \( y \)-values for the given \( x \)-values: \( x = -3, -2, -1, 0, 1, 2, 3 \).

### Step-by-Step Solution:

1. **Understand the Equation**: The equation \( y = |x| - 2 \) involves the absolute value function \( |x| \), which always returns a non-negative value. The term \( -2 \) shifts the graph downward by 2 units.

2. **Calculate \( y \)-values**:
   - For \( x = -3 \): 
     \[
     y = |-3| - 2 = 3 - 2 = 1
     \]
   - For \( x = -2 \): 
     \[
     y = |-2| - 2 = 2 - 2 = 0
     \]
   - For \( x = -1 \): 
     \[
     y = |-1| - 2 = 1 - 2 = -1
     \]
   - For \( x = 0 \): 
     \[
     y = |0| - 2 = 0 - 2 = -2
     \]
   - For \( x = 1 \): 
     \[
     y = |1| - 2 = 1 - 2 = -1
     \]
   - For \( x = 2 \): 
     \[
     y = |2| - 2 = 2 - 2 = 0
     \]
   - For \( x = 3 \): 
     \[
     y = |3| - 2 = 3 - 2 = 1
     \]

### Completed Table:
|  \( x \)  | \( y \)  |
|:---------:|:--------:|
|   -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 \( y = |x| - 2 \).

Would you like any further details or have any questions? 

Here are some related questions to deepen your understanding:

1. How does the graph of \( y = |x| - 2 \) compare to the graph of \( y = |x| \)?
2. What effect does adding or subtracting a constant from \( |x| \) have on its graph?
3. How would the graph change if the equation was \( y = |x + 1| - 2 \)?
4. What are the key features of the graph of an absolute value function?
5. Can you generalize the shape of \( y = |x| + c \) for any constant \( c \)?

**Tip**: Remember that the absolute value function \( |x| \) is V-shaped and symmetrical about the y-axis. Adjusting it vertically shifts the entire graph up or down.

Graph the equation y = |x| - 2. Find the following y-values. Then choose the correct graph of the equation.

Learn how to graph the absolute value function y = |x| - 2 by finding the corresponding y-values for x-values ranging from -3 to 3. This problem is perfect for students in Grades 6-8 and covers key concepts related to graphing linear equations and understanding absolute value functions.

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