Understanding the Square Root Function: Explained Step by Step

y = √x

To understand this equation, let’s break it down step by step

To understand this equation, let’s break it down step by step.

The equation y = √x represents a square root function, where x is the input variable and y is the output variable.

The square root (√) of a number x is a value y such that y * y = x. In other words, when you square the value of y, you get x.

Let’s look at some examples to illustrate how this equation works:

1. For x = 0, y = √0 = 0. Here, the square root of 0 is 0.

2. For x = 1, y = √1 = 1. The square root of 1 is 1.

3. For x = 4, y = √4 = 2. The square root of 4 is 2.

4. For x = 9, y = √9 = 3. The square root of 9 is 3.

In general, when x is positive, the square root function yields positive values for y. However, if we have a negative value for x (e.g., x = -1), the equation y = √x does not have a real number solution. In such cases, the square root of a negative number is known as an imaginary number.

Graphically, the square root function produces a curve called a square root curve or a radical curve. The curve starts at the point (0, 0) and extends infinitely upwards.

The square root function has several properties worth noting:

1. Domain: The domain of the function y = √x includes only non-negative real numbers or zero (x ≥ 0).

2. Range: The range of the function includes only non-negative real numbers or zero (y ≥ 0).

3. Increasing function: As x increases, the value of y also increases. The square root function is always positive (ignoring imaginary solutions).

4. Vertical symmetry: The graph of y = √x is symmetric with respect to the y-axis. This means that if we reflect any point on the graph across the y-axis, we obtain another point on the graph.

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