The graph of y = ln x is the mirror image of y = eˣ in the line y = x. It rises slowly and dives down towards the y-axis.
| Domain | (0, ∞) |
| Range | All real numbers (ℝ) |
| Symmetry | Neither even nor odd |
| Increasing / decreasing | Increasing on (0, ∞) |
| Key feature | Crosses the x-axis at (1, 0); asymptote x = 0 |
In y = a ln(x − h) + k, the asymptote moves to x = h and the point (1, 0) moves to (h + 1, 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 ln x?Play Vakra: name the curve in five plots