Y is equal to the root of x graph. Power function and roots - definition, properties and formulas. Properties of the function y=√x
Square root as an elementary function.
Square root is an elementary function and a special case of a power function for . The arithmetic square root is smooth at , and at zero it is right continuous but not differentiable.
As a function, a complex variable root is a two-valued function whose leaves converge at zero.
Graphing the square root function.
- Filling out the data table:
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2. We plot the points that we received on the coordinate plane.
3. Connect these points and get a graph of the square root function:
Transforming the graph of a square root function.
Let us determine what function transformations need to be made in order to construct function graphs. Let's define the types of transformations.
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Conversion type |
Conversion |
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Transferring a function along an axis OY for 4 units up. |
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internal |
Transferring a function along an axis OX for 1 unit to the right. |
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internal |
The graph approaches the axis OY 3 times and compresses along the axis OH. |
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The graph moves away from the axis OX OY. |
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internal |
The graph moves away from the axis OY 2 times and stretched along the axis OH. |
Often, function transformations are combined.
For example, you need to plot the function 
. This is a square root graph that needs to be moved one unit down the axis OY and one unit to the right along the axis OH and at the same time stretching it 3 times along the axis OY.
It happens that immediately before constructing a graph of a function, preliminary identity transformations or simplifications of functions are needed.
Consider the function y=√x. The graph of this function is shown in the figure below.
Graph of the function y=√x
As you can see, the graph resembles a rotated parabola, or rather one of its branches. We get a branch of the parabola x=y^2. It can be seen from the figure that the graph touches the Oy axis only once, at the point with coordinates (0;0).
Now it is worth noting the main properties of this function.
Properties of the function y=√x
1. The domain of definition of a function is a ray.
Answer. D(f) = [-1.4].
A.G. Mordkovich Algebra 10th grade
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