Question

Исследование функции y=((2х-1)^2)/(2+х) срочно пожалуйста

Answer 1

Решение дано в приложении.

Answer 2

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

Let's analyze the function \( y = \frac{{(2x-1)^2}}{{2+x}} \).

1. Domain and Range: - The domain of the function is all real numbers except for the value that makes the denominator zero. - The range of the function depends on the domain and the behavior of the function.

2. Symmetry: - The function may exhibit symmetry, which can be determined by analyzing its equation.

3. Intercepts: - The x-intercept(s) can be found by setting y = 0 and solving for x. - The y-intercept can be found by setting x = 0 and solving for y.

4. Asymptotes: - The function may have vertical, horizontal, or slant asymptotes, which can be determined by analyzing the behavior of the function as x approaches certain values.

5. Critical Points and Extrema: - Critical points can be found by setting the derivative of the function equal to zero and solving for x. - Extrema can be determined by analyzing the behavior of the function at the critical points.

6. Concavity and Inflection Points: - The concavity of the function can be determined by analyzing the second derivative of the function. - Inflection points can be found by analyzing the behavior of the function where the concavity changes.

7. Sketching the Graph: - By combining the information obtained from the above analysis, a rough sketch of the graph of the function can be made.

Let's proceed with the analysis based on the given function.