f(x) = √x
The function f(x) = √x represents the square root function
The function f(x) = √x represents the square root function. In this function, the input value is x, and the output value is the square root of x.
To understand the square root function, it is helpful to know a few key concepts:
1. Square Root: The square root of a number x is a value that, when multiplied by itself, gives x. For example, the square root of 9 is 3 because 3 * 3 = 9. The square root is denoted by the √ symbol.
2. Domain: The domain of the square root function is the set of all non-negative real numbers (x ≥ 0). Since you cannot take the square root of a negative number, the function is not defined for negative values of x.
3. Range: The range of the square root function is the set of all non-negative real numbers (y ≥ 0). Since the square root of a non-negative number is always non-negative, the output values of the function are always non-negative.
Graphically, the square root function produces a curve known as a square root curve. When graphed, the curve starts at the origin (0,0) and extends indefinitely in the positive y-direction. The curve gets steeper as x increases, but it never dips below the x-axis due to the non-negativity of the range.
For example, let’s evaluate the function f(x) = √x for some specific values of x:
1. f(0) = √0 = 0: The square root of 0 is 0.
2. f(4) = √4 = 2: The square root of 4 is 2.
3. f(9) = √9 = 3: The square root of 9 is 3.
4. f(16) = √16 = 4: The square root of 16 is 4.
As you can see, the value of f(x) increases as x increases, but it always remains non-negative.
So, if you have any specific questions or need further explanations about the square root function, feel free to ask!
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