The graph of y = |x| is a V-shape: y = −x on the left of the origin and y = x on the right.
| Domain | All real numbers (ℝ) |
| Range | [0, ∞) |
| Symmetry | Even: symmetric about the y-axis |
| Increasing / decreasing | Decreasing on (−∞, 0], increasing on [0, ∞) |
| Key feature | Sharp corner at (0, 0); not differentiable there |
In y = a|x − h| + k, the corner moves from (0, 0) to (h, k).
a stretches the graph vertically and flips it when negative. h shifts it right (left when negative). k shifts it up (down when negative).
Can you spot a transformed |x|?Play Vakra: name the curve in five plots