Question

Постройте гра­фик функции ((x^2-5x+3)^2)/(x-3). Пожалуйста помогите!!!

Answer 1

ДАНО
$Y(x)= \frac{(x^2-5x+3)^2}{x-3}$
ПОСТРОИТЬ ГРАФИК.
Рисунок с графиком - в приложении.
1. Область определения - Х≠3 - вертикальная асимптота.

Answer 2

Plotting the Function ((x^2-5x+3)^2)/(x-3)

To plot the function ((x^2-5x+3)^2)/(x-3), we can start by analyzing the equation and identifying any critical points or asymptotes.

The function is given by:

f(x) = ((x^2-5x+3)^2)/(x-3)

To plot the function, we can follow these steps:

1. Determine the domain of the function: In this case, the function is defined for all real numbers except x = 3, as the denominator cannot be zero.

2. Find the critical points: Critical points occur when the derivative of the function is zero or undefined. Let's find the derivative of the function:

f'(x) = (2(x^2-5x+3)(2x-5))/(x-3)^2

Setting the derivative equal to zero and solving for x, we get:

2(x^2-5x+3)(2x-5) = 0

This equation gives us two critical points: x = 5/2 and x = 3.

3. Determine the behavior of the function around the critical points: To do this, we can analyze the sign of the derivative in the intervals defined by the critical points and the domain.

- For x < 5/2, the derivative is negative, indicating that the function is decreasing. - For 5/2 < x < 3, the derivative is positive, indicating that the function is increasing. - For x > 3, the derivative is negative, indicating that the function is decreasing.

4. Find any vertical asymptotes: Vertical asymptotes occur when the denominator of the function is zero. In this case, the function has a vertical asymptote at x = 3.

Now, let's plot the function using this information.

Plot:

Unfortunately, I am unable to generate a plot here. However, you can use graphing software or online graphing tools to plot the function ((x^2-5x+3)^2)/(x-3). Simply input the function into the graphing tool, and it will generate the plot for you.

I hope this helps! Let me know if you have any further questions.