Graphing the Square Root Function | A Step-by-Step Guide and Key Considerations

Graph of Square Root Parent Function

The graph of the square root function, or the square root parent function, is a curve that starts at the point (0, 0) and continues to increase as you move to the right

The graph of the square root function, or the square root parent function, is a curve that starts at the point (0, 0) and continues to increase as you move to the right. This function is represented by the equation y = √x.

To graph the square root parent function, you can start by creating a table of values. Choose a few x-values that are greater than or equal to 0, and calculate the corresponding y-values by taking the square root of the x-values.

For example, if we choose x = 0, 1, 4, 9, and 16, the corresponding y-values are:

x = 0 → y = √0 = 0
x = 1 → y = √1 = 1
x = 4 → y = √4 = 2
x = 9 → y = √9 = 3
x = 16 → y = √16 = 4

Now, plot these points on a graph, with the x-values on the horizontal axis and the y-values on the vertical axis. You should have the points (0, 0), (1, 1), (4, 2), (9, 3), and (16, 4).

Next, draw a smooth curve that passes through these points. This curve represents the graph of the square root parent function. It should start at the origin (0, 0) and increase as x increases.

Remember that the square root function is only defined for non-negative values of x. This means the graph only exists for x ≥ 0. Also, note that the graph is continuous, meaning there are no breaks or gaps in the curve.

It’s important to note that this graph is the basic shape of the square root function. Any transformations, such as shifts, stretches, or reflections, will change the position or shape of the graph accordingly.

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