Explain the difference between square root functions

A square root function is a type of mathematical function that represents the inverse operation of squaring a number. The square root of a number, denoted by the symbol √, is the value that, when multiplied by itself, gives the original number.

To understand the difference between square root functions, it is helpful to consider their equations and characteristics.

The two main types of square root functions are square root functions with a positive square root symbol (√) and square root functions with a negative square root symbol (-√).

1. Positive Square Root Function (√)
The positive square root function is represented by the equation y = √x. In this function, the y-coordinate (output) is the square root of the x-coordinate (input). For example, if x = 9, then y = √9 = 3. The positive square root function returns the positive solution.

2. Negative Square Root Function (-√)
The negative square root function is represented by the equation y = -√x. In this function, the y-coordinate (output) is the negative square root of the x-coordinate (input). For example, if x = 9, then y = -√9 = -3. The negative square root function returns the negative solution.

So, the main difference between square root functions is the sign of the square root symbol (√). The positive square root function returns the positive square root, while the negative square root function returns the negative square root.

To graph these functions or evaluate specific values, you can follow these steps:
1. Determine the type of square root function (positive or negative).
2. Substitute the x-values into the appropriate equation.
3. Calculate the square root of each x-value to get the corresponding y-values.
4. Plot the points (x, y) on a coordinate plane to graph the function.

Remember to consider any restrictions on the domain of the function. Square root functions are defined for non-negative values of x, so the domain usually includes all real numbers greater than or equal to zero (x ≥ 0).