Question

Срочно!!! Побудуйте графік функції y=(x-x2)/|x| ​

Answer 1

Ответ во вложении сверху

Answer 2

Graph of the Function y=(x-x^2)/|x|

To graph the function y=(x-x^2)/|x|, we can start by analyzing the equation and identifying key points and characteristics.

The function y=(x-x^2)/|x| can be simplified as follows: - When x is positive, |x| is equal to x, so the equation becomes y=(x-x^2)/x. - When x is negative, |x| is equal to -x, so the equation becomes y=(x-x^2)/(-x).

Now, let's analyze the behavior of the function for different values of x.

1. When x is positive: - As x approaches 0 from the positive side, the denominator x approaches 0, causing the function to approach positive infinity. - As x approaches positive infinity, both the numerator and denominator approach infinity, resulting in the function approaching 1.

2. When x is negative: - As x approaches 0 from the negative side, the denominator -x approaches 0, causing the function to approach negative infinity. - As x approaches negative infinity, both the numerator and denominator approach negative infinity, resulting in the function approaching -1.

Based on this analysis, we can conclude that the function has a vertical asymptote at x=0 and two horizontal asymptotes at y=1 and y=-1.

To graph the function, we can plot some key points and use the behavior analysis to sketch the curve.

Key Points:

To find some key points, we can substitute different values of x into the equation and calculate the corresponding y-values.

1. When x=1: - Substituting x=1 into the equation, we get y=(1-1^2)/|1| = 0/1 = 0. - So, we have the point (1, 0).

2. When x=-1: - Substituting x=-1 into the equation, we get y=(-1-(-1)^2)/|-1| = (-1-1)/1 = -2/1 = -2. - So, we have the point (-1, -2).

3. When x=2: - Substituting x=2 into the equation, we get y=(2-2^2)/|2| = (2-4)/2 = -2/2 = -1. - So, we have the point (2, -1).

Now, let's plot these points and sketch the curve based on the behavior analysis.

Graph:


Please note that the graph provided is a rough sketch and may not be to scale. It is always recommended to use graphing software or a graphing calculator for accurate representations of functions.

I hope this helps! Let me know if you have any further questions.