Question

Построить график y=|x^2+3x+2|/|х+1| Помогите пожалуйста ))

Answer 1

Разложим на множители  x^2+3x+2=0; D=9-4*1*2=9-8=1; x1=(-3-1)/2=-2; x2=(-3+1)/2=-1
x^2+3x+2=(x+2)(x+1);
|x^2+3x+2| / |x+1|=|x+1)(x+2)| /|x+1|=|x+2|
y=|x+2|
строим у=|x| -угол с вершиной (0;0), а стороны его биссектрисы 1 и 2четвертей
Потом переносим его вдоль оси х влево на 2 клетки!





















\

Answer 2

Plotting the Graph of y = |x^2 + 3x + 2| / |x + 1|

To plot the graph of the function y = |x^2 + 3x + 2| / |x + 1|, we can start by analyzing the behavior of the function for different values of x.

Let's break down the steps to plot the graph:

1. Determine the critical points: - The critical points occur when the denominator, |x + 1|, equals zero. This happens when x = -1. - So, we have a vertical asymptote at x = -1.

2. Analyze the behavior of the function: - For x < -1, the expression inside the absolute value signs, x^2 + 3x + 2, is negative. Therefore, the function becomes y = -(x^2 + 3x + 2) / (x + 1). - For -1 < x < 0, the expression inside the absolute value signs, x^2 + 3x + 2, is positive. Therefore, the function remains y = (x^2 + 3x + 2) / (x + 1). - For x > 0, the expression inside the absolute value signs, x^2 + 3x + 2, is positive. Therefore, the function remains y = (x^2 + 3x + 2) / (x + 1).

3. Find the y-intercept: - To find the y-intercept, substitute x = 0 into the function: y = |0^2 + 3(0) + 2| / |0 + 1| = 2 / 1 = 2. - So, the y-intercept is (0, 2).

4. Plot the graph: - Based on the analysis above, we can plot the graph as follows:


- The graph has a vertical asymptote at x = -1 and passes through the point (0, 2).

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