Maths
Show me the graph of power function y=x²
and out to dimain and range
To plot the graph of the power function y = x^2, you can choose some values for x and calculate the corresponding values for y.
Here are some points you can use:
x | y
-----------
-3 | 9
-2 | 4
-1 | 1
0 | 0
1 | 1
2 | 4
3 | 9
Based on these points, you can plot the graph of y = x^2. The graph will be a U-shaped curve opening upwards. The vertex of the graph is at the point (0, 0).
The domain of the power function y = x^2 is all real numbers since any real number can be squared.
The range of the power function y = x^2 is all non-negative real numbers (including zero), since squaring any real number always gives a non-negative result.
Here is a visual representation of the graph of y = x^2:
```plaintext
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| **
| * *
| * *
| * *
| * *
| * *
| * *
| * *
*------------------*
|
```
In this graph, the x-axis represents the values of x, and the y-axis represents the values of y. The curve represents the graph of y = x^2.
To plot the graph of the power function y = x², you can follow these steps:
Step 1: Choose a set of x-values that you want to use for plotting the graph. For example, you can choose x-values that range from -5 to 5.
Step 2: Substitute each chosen x-value into the equation y = x² to find the corresponding y-value. For example, if x = -5, then y = (-5)² = 25. Repeat this for all the chosen x-values.
Step 3: Plot the coordinates (x, y) on a graph paper. Use the x-values as the horizontal axis and the corresponding y-values as the vertical axis.
Step 4: Connect the plotted points with a smooth curve to obtain the graph of the power function y = x².
The domain of the power function y = x² is the set of all real numbers since there are no restrictions on the values of x.
The range of the power function y = x² is the set of all real numbers greater than or equal to 0. This is because squaring any real number will always result in a non-negative value.
Here is an example graph showing the power function y = x²:
```
|
9| *
| *
8| *
| *
7| *
| *
6| *
| *
5| *
| *
4| *
| *
3| *
| *
2| *
| *
1| *
| *
0| *
| *
-1| *
| *
-2| *
| *
-3| *
| *
-4| *
|*
---------------------------------
-5 -4 -3 -2 -1 0 1 2 3 4 5
```
Note: The above graph is just an example shape of the power function y = x². The scale and shape of the graph may vary depending on the range of x-values you choose and the scale of the graph paper.
To graph the power function y = x², you can follow these steps:
1. Choose a set of values for the independent variable x. In this case, let's choose some values for x such as -3, -2, -1, 0, 1, 2, and 3.
2. Substitute each value of x into the equation y = x² to find the corresponding values of y. For example, if x = 2, then y = 2² = 4.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the points with a smooth curve to create the graph of the power function y = x².
The domain and range of the power function y = x² can be determined from the graph:
- Domain: The domain of a power function is the set of all possible x-values for which the function is defined. In this case, since the graph extends infinitely in both directions along the x-axis, the domain of y = x² is (-∞, +∞), which means all real numbers.
- Range: The range of a power function is the set of all possible y-values that the function can take. The graph of y = x² is symmetric about the y-axis, opening upwards, and it always remains above or on the x-axis. Therefore, the range is [0, +∞), which means all non-negative real numbers.
To see a visual representation of the graph and understand it better, you can use graphing tools or online graphing calculators by plotting the power function y = x². These tools will automatically display the graph and provide the domain and range information.
I hope this helps! Let me know if you have any further questions.