Square Root Parent Function
Domain: (-∞, ∞) Range: (0, ∞)
The square root parent function is a mathematical function typically denoted as f(x) = sqrt(x), where x represents a real number greater than or equal to zero. The graph of the square root parent function is a curve that starts at the origin and continues to increase as x increases. The resulting curve is S-shaped and continues indefinitely to the right.
The square root parent function represents a relationship between a variable and its square root. It is commonly used in geometry, physics, engineering, and other fields. The curve of the function is useful in modeling certain types of natural phenomena, such as population growth or radioactive decay.
The most basic properties of the square root parent function are:
1. Domain: The domain of the square root parent function is x≥ 0, which means that it is defined only for non-negative values of x.
2. Range: The range of the square root parent function is y≥ 0.
3. Intercepts: The square root parent function intercepts the y-axis at (0, 0), and does not intercept the x-axis.
4. Symmetry: The square root parent function is not symmetric around the origin, that is, it does not possess any axis of symmetry.
5. Continuity: The square root parent function is continuous for all values of x greater than or equal to zero.
6. Differentiability: The square root parent function is differentiable for all values of x greater than zero.
7. Increasing: The square root parent function is an increasing function, which means that as x increases, y increases as well.
These properties make the square root parent function a useful tool for solving certain types of mathematical problems.
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