Relationship Between √(x²) and |x|
These equations are equivalent, representing the same relationship:
√(x²) = |x|
Table of Points:
| x | √(x²) | |x| |
|---|---|---|
| -3 | 3 | 3 |
| -2 | 2 | 2 |
| -1 | 1 | 1 |
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 3 | 3 | 3 |
As shown in the table, for any real value of x, √(x²) is equal to |x|, demonstrating their equivalence.
These equations form a V-shaped graph along the x-axis.
The graphs of √(x²) and |x| are representations of mathematical functions with distinct characteristics:
Graph of √(x²):
Calculates the square root of x², always resulting in non-negative values.
Forms a V-shaped graph along the x-axis.
Vertex at the origin (0,0) and extends infinitely in both directions along the x-axis.
Graph of |x|:
Represents the absolute value of x, which is always non-negative.
Also forms a V-shaped graph along the x-axis.
Vertex at the origin (0,0) and extends infinitely in both directions along the x-axis.
Both functions yield the same result for any real value of x, resulting in identical graphs.
