Square Root Parent Function
Domain: (-∞, ∞) Range: (0, ∞)
The square root parent function is a mathematical function with the formula f(x) = √x. This function is a basic example of a non-linear function. It is called a parent function because other functions can be derived from it by changing its parameters.
The graph of the square root parent function is a curve that starts at the origin and extends towards the right. As x increases, the curve becomes steeper. The graph is continuous and its domain is x ≥ 0, while its range is y ≥ 0.
The square root parent function has a few important features:
1. Domain: The domain of the function is x ≥ 0. This means that the function is only defined for non-negative values of x.
2. Range: The range of the function is y ≥ 0. This means that all values of y that are produced by the function are non-negative.
3. Asymptote: The function has a vertical asymptote at x = 0. This means the function approaches infinity as it approaches zero from the right.
4. Symmetry: The square root parent function is an odd function. This means that it exhibits symmetry about the origin.
5. Smoothness: The square root parent function is a continuous and smooth curve.
The square root parent function is useful in many applications, such as in modeling the relationship between the area of a circle and its radius or the distance traveled by an object under constant acceleration.
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