Question

Помогите, пожалуйста. Как построить такой график функции? y=(x^2-16)/(2x+8)

Answer 1

ОДЗ:  (-∞;-4)∨(-4;+∞)
y=(x-4)(x+4)/2(x+4)=x/2-2
х  0    4
у -2    0
Построить прямую по точкам и выколоть точку на графике с координатами (-4;-4)

Answer 2

Graph of the Function y=(x^2-16)/(2x+8)

To graph the function y=(x^2-16)/(2x+8), we can follow these steps:

1. Identify the Vertical Asymptotes: - The function has a vertical asymptote where the denominator equals zero. In this case, the vertical asymptote occurs when 2x + 8 = 0. Solving for x, we get x = -4.

2. Identify the Horizontal Asymptotes: - To find the horizontal asymptote, we can use the fact that as x approaches positive or negative infinity, the function approaches the ratio of the leading coefficients of the numerator and denominator. In this case, the horizontal asymptote is y = x/2.

3. Plot Key Points: - We can plot key points to understand the behavior of the function. For example, when x = -6, -4, -2, 0, 2, and 4, we can calculate the corresponding y values.

4. Sketch the Graph: - Using the information from the vertical and horizontal asymptotes, along with the key points, we can sketch the graph of the function.

Let's proceed with plotting the graph of the function y=(x^2-16)/(2x+8).