Question

Исследуйте функцию на четность: у=х^2|х^3|+х^4 пожалуйста!!!

Answer 1

Y=(-x)^2*|(-x)^3|+(-x)^4= x^2*|x^3|+x^4-функция четная

Answer 2

Exploring the Function for Parity

To explore the function for parity, let's consider the function y = x^2 | x^3 | + x^4.

The function can be broken down into three parts: 1. x^2 2. x^3 3. x^4

Let's analyze the parity of each part separately and then combine the results to determine the overall parity of the function.

Parity of x^2

The function x^2 is an even function because for any value of x, x^2 = (-x)^2. This means that x^2 is symmetric about the y-axis and has even parity.

Parity of x^3

The function x^3 is an odd function because for any value of x, x^3 = -(-x)^3. This means that x^3 is symmetric about the origin and has odd parity.

Parity of x^4

The function x^4 is an even function because for any value of x, x^4 = (-x)^4. This means that x^4 is symmetric about the y-axis and has even parity.

Overall Parity of the Function

To determine the overall parity of the function y = x^2 | x^3 | + x^4, we need to consider the combination of the parities of the individual parts.

The addition of an even and an odd function results in an odd function. Therefore, the function x^2 | x^3 | is odd.

Adding an odd function to an even function results in an odd function. Therefore, the overall function y = x^2 | x^3 | + x^4 is an odd function.

This means that the function is symmetric about the origin and has odd parity.

Conclusion

In conclusion, the function y = x^2 | x^3 | + x^4 is an odd function, exhibiting symmetry about the origin and having odd parity.