What Does a Square Root Function Look Like?
What Does a Square Root Function Look Like?
The square root function is written as y = √x. Its graph starts at the origin (0, 0) and curves upward to the right, getting progressively flatter.
Key properties
- Domain: x ≥ 0 (only defined for non-negative numbers)
- Range: y ≥ 0 (always outputs non-negative values)
- Starting point: (0, 0)
- Shape: Concave down — grows fast at first, then slows
- Inverse: It is the inverse of y = x² (for x ≥ 0)
Key points on the graph
- (0, 0) · (1, 1) · (4, 2) · (9, 3) · (16, 4) · (25, 5) · (100, 10)
y = √x = x^(1/2)
The square root function grows without bound but increasingly slowly. As x → ∞, y → ∞, but the rate of growth (slope) decreases, approaching zero.