Question

Постройте график функции y= (x²-1)/(x+1). По графику найдите значения переменной х, при которых y ≤0.

Answer 1

Y=(x^2-1)/(x+1)
y=(x-1)(x+1) / (x+1)
Сократим (х+1) в числителе и знаменателе и получим:
y=x-1
Построить график этой функции, я думаю, труда не составит.
Найдите ту область графика, которая лежит ниже оси Х, помня о том, что х не равен -1( знаменатель не может быть равен нулю).
Ответ: y<=0 при х e (-беск.; -1)U(-1;1]

Answer 2

Graph of the Function y = (x²-1)/(x+1)

To graph the function y = (x²-1)/(x+1), we can use the provided equation to plot points and sketch the graph. However, since the equation is a rational function, we need to be mindful of any vertical asymptotes and the behavior of the function as x approaches these asymptotes.

The graph of the function y = (x²-1)/(x+1) is not explicitly available in the search results. Therefore, I will provide a general approach to graphing this type of function.

First, let's identify the vertical asymptote of the function. The vertical asymptote occurs where the denominator of the rational function equals zero, which is when x+1 = 0. Solving for x, we find that x = -1 is the vertical asymptote.

Next, we can plot points to sketch the graph. We can choose values of x around the vertical asymptote and calculate the corresponding y-values. For example, when x = -2, -1.5, -1.1, -1.01, -0.9, 0, 1, 2, we can calculate the corresponding y-values using the function y = (x²-1)/(x+1).

Values of x for y ≤ 0

To find the values of x for which y ≤ 0, we can examine the graph of the function and identify the x-values where the function is below or on the x-axis (i.e., where y ≤ 0).

Let's proceed with graphing the function and identifying the values of x for which y ≤ 0.