Graph of y = sqrt(x)
Interactive graph of y = sqrt(x) (square root of x). Explore the half-parabola, its domain restriction, and concavity with our free graphing calculator.
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Understanding the Function
The square root function y = sqrt(x) is the inverse of y = x² restricted to non-negative values. Its graph is a curve that starts at the origin and increases to the right, growing more slowly as x increases. It looks like the top half of a sideways parabola.
Because you cannot take the square root of a negative number in the real number system, the domain is restricted to x >= 0 and the range is y >= 0. The function is concave down everywhere on its domain, meaning it curves toward the x-axis as x grows, never leveling off completely but growing increasingly slowly.
Key properties: domain [0, infinity), range [0, infinity), passes through (0, 0), (1, 1), and (4, 2). The derivative is 1/(2*sqrt(x)), which is undefined at x = 0, indicating a vertical tangent line at the origin. The function grows proportionally to x^(1/2).