Question

постройте график функции y= ( x-1/ x^2 - x) + 1

Answer 1

http://lmgtfy.com/?q=y%3D+(+x-1%2F+%20x%5E2+-+x)+%2B+1

Вот ,построенный гуглом график

Answer 2

Graph of the Function y = (x-1)/(x^2 - x) + 1

To graph the function y = (x-1)/(x^2 - x) + 1, we can start by analyzing the equation and identifying any important characteristics.

The function can be rewritten as y = (x-1)/(x(x-1)) + 1. Notice that the denominator contains a common factor of (x-1), which means that the function is undefined at x = 1. This is because dividing by zero is not allowed in mathematics.

Now, let's analyze the behavior of the function as x approaches positive and negative infinity. As x becomes very large (positive or negative), the terms (x-1) and x^2 dominate the function. Since the degree of the numerator and denominator is the same (both are quadratic), the function approaches a horizontal asymptote.

To determine the horizontal asymptote, we can divide the leading terms of the numerator and denominator. In this case, the leading terms are x/x^2, which simplifies to 1/x. As x approaches positive or negative infinity, 1/x approaches zero. Therefore, the horizontal asymptote of the function is y = 1.

Now, let's plot the graph of the function:


As we can see from the graph, the function has a vertical asymptote at x = 1, where it is undefined. The function approaches the horizontal asymptote y = 1 as x approaches positive or negative infinity.

Please note that the graph is a visual representation and may not be completely accurate. It is always recommended to use graphing software or calculators for precise graphs.

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