Understanding the Square Root Function: Examples, Properties, and Graphing

y = √x

The equation y = √x represents a square root function

The equation y = √x represents a square root function. In this equation, x is the input or independent variable, and y is the output or dependent variable. When you input a value for x, the function will give you the corresponding value of y.

To understand how this equation works, let’s go through a few examples:

Example 1:
If x = 4, we can substitute this value into the equation:
y = √4
In this case, the square root of 4 is 2. Therefore, y = 2.

Example 2:
Suppose x = 9:
y = √9
The square root of 9 is 3, so y = 3.

Example 3:
If x = 16:
y = √16
The square root of 16 is 4, so y = 4.

You can see that for any positive value of x, the value of y will be the square root of x.

Now, let’s consider some properties of the square root function:

1. Domain: The domain of the square root function is all non-negative real numbers. This means that x must be greater than or equal to zero.

2. Range: The range of the square root function is all non-negative real numbers. The value of y (square root) is always non-negative.

3. Symmetry: The graph of the square root function is symmetric about the y-axis. This means that if (x, y) is a point on the graph, then (-x, y) is also a point on the graph.

4. Increasing function: The square root function is an increasing function. This means that as x increases, the value of y also increases.

To graph the square root function, you can start by plotting some points and connecting them with a smooth curve. For example, for x = 0, y = 0, for x = 1, y = 1, for x = 4, y = 2, and so on. You will notice the resulting graph is a curve that starts from the origin and increases as x increases.

I hope this explanation helps you understand the square root function. If you have any further questions or need clarification, feel free to ask.

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