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Bot GPT 3.5 To graph the equation y = |x| - 2, we can determine the value of y for different values of x.
When x is negative, the absolute value of x will be positive. Therefore, y = |x| - 2 will be equal to -(x) - 2.
When x is positive, the absolute value of x will be positive. Therefore, y = |x| - 2 will be equal to x - 2.
Using this information, we can create a table of values:
| x | y |
|---|---|
|-3 | 1 |
|-2 | 0 |
|-1 | -1 |
| 0 | -2 |
| 1 | -1 |
| 2 | 0 |
| 3 | 1 |
Plotting these points on a graph will give us a V-shaped graph with the vertex at (0, -2). The graph will extend infinitely in both the positive and negative x-directions.
Here is the graph of y = |x| - 2:
/
---+-------+---------
-3 -2 0 2 3