Question

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

Answer 1

Область определения функции - (-∞;1)∪(1;+∞)
Преобразуем формулу:
$y= \frac{x^2-1}{x-1} = \frac{(x-1)(x+1)}{x-1} =x+1$
Строим график прямой у = х+1 и на нём исключаем точку с абсциссой х = 1.
Чертеж во вложении.

Answer 2

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

To graph the function y = (x^2-1)/(x-1), we can start by analyzing its behavior and then plot the graph based on the given equation.

Behavior Analysis: The function y = (x^2-1)/(x-1) has a vertical asymptote at x = 1, as the denominator becomes zero at this point. It also has a hole at x = 1, as the factor (x-1) cancels out in the numerator and denominator.

Graph Plotting: We can plot the graph of the function by considering the behavior around x = 1 and the overall shape of the function.

Graph: The graph of the function y = (x^2-1)/(x-1) is a hyperbola with a vertical asymptote at x = 1 and a hole at the same point.


This graph represents the behavior of the given function y = (x^2-1)/(x-1) based on the provided equation.