Understanding the Square Root Function: Properties, Range, and Graph

square root function

The square root function, denoted by √x or √(x), is a mathematical function that gives the value which, when multiplied by itself, gives the number x

The square root function, denoted by √x or √(x), is a mathematical function that gives the value which, when multiplied by itself, gives the number x.

The square root function is typically defined for non-negative real numbers. The value of √x is always positive or zero. For example, the square root of 4 is 2, because 2×2 = 4, and the square root of 9 is 3, because 3×3 = 9.

The basic properties of square root function are as follows:

1. The domain of the square root function is all non-negative real numbers, [0, ∞). This is because the square root of a negative number is undefined in the real number system.

2. The range of the square root function is also all non-negative real numbers, [0, ∞). As mentioned earlier, the value of √x is always positive or zero.

3. The square root function is an increasing function, which means that as the input increases, the output also increases. For example, as you go from 0 to 1, the square root value increases from 0 to 1. Similarly, as you go from 4 to 9, the square root value increases from 2 to 3.

4. The square root function has a vertical asymptote at x = 0. As x approaches 0 from the positive side, the value of √x approaches 0.

5. The square root function is not defined for negative values of x in the real number system. However, in the complex plane, the square root of a negative number can be defined using imaginary numbers. For example, √(-4) is equal to 2i, where i is the imaginary unit (√(-1)).

6. The square root function is the inverse of the square function (x^2). This means that if you take the square root of a number and then square it, you will get back the original number.

To graph the square root function, you can plot points by choosing various x-values and finding their corresponding y-values (square roots). Another approach is to recognize the symmetrical shape of the graph – it starts at the origin (0,0) and curves upward as x increases.

Overall, the square root function is a fundamental mathematical function with various applications in areas such as geometry, physics, engineering, and finance.

More Answers: