Exploring the Properties of the Square Root Function: Domain, Range, Graph, and Important Properties

f(x)=√x

The function f(x) = √x represents a square root function

The function f(x) = √x represents a square root function. It gives the square root of any given input value of x.

To better understand the properties of this function, let’s look at some important points:

1. Domain: The domain of a square root function is the set of all non-negative real numbers because we cannot take the square root of a negative number. Therefore, the domain of f(x) = √x is x ≥ 0.

2. Range: The range of the square root function is all non-negative real numbers as well. This means that the outputs of the function, or y-values, will always be greater than or equal to 0.

3. Graph: The graph of f(x) = √x is a curve that starts at the origin (0,0) and continually rises as x increases. The shape of the graph is a half parabola that opens to the right. As x approaches infinity, the graph also approaches infinity, but at a slower rate. Similarly, as x approaches negative infinity, the graph approaches negative infinity, but again at a slower rate.

4. Properties: One important property of the square root function is that if you square the function’s output, it will give you the original input. In other words, if f(x) = √x, then (f(x))^2 = x. For example, if f(x) = √4, then (f(x))^2 = (2)^2 = 4.

It’s also worth noting that the square root function is an example of an odd function because of its symmetry across the origin. This means that f(-x) = -f(x) for all x in the domain.

I hope this explanation helps. Let me know if you have any further questions!

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