Question

Как построить график функции у=(2х-12)/(х-3)

Answer 1

1) Раскрыть скобки:
у=2х²-18х+36- парабола, ветви которой направленны вверх.
2)Находим координаты вершины параболы:
х=-b/2а=18/4=4,5
у=2*4,5²-18*4,5+36=-5,5
Точка (4,5;-5,5)-вершина параболы
3) Затем составляем таблицу значений:
х 2   3    4   4,5    5   6  7
у 8   0  -4  -5,5  -4   0  8 
Стоим точки и соеденяем. Получается парабола.

Answer 2

Building a Graph for the Function u=(2x-12)/(x-3)

To build a graph for the function u=(2x-12)/(x-3), we can follow these steps:

1. Identify the Key Points: - We need to identify the key points of the function, such as the x and y-intercepts, vertical asymptotes, horizontal asymptotes, and any other relevant points.

2. Plot the Points: - After identifying the key points, we can plot them on the graph.

3. Draw the Graph: - Using the plotted points, we can draw the graph of the function.

Key Points of the Function

1. X-Intercept: - The x-intercept is the point where the graph crosses the x-axis. It occurs when y=0. - To find the x-intercept, we can set u=0 and solve for x.

2. Y-Intercept: - The y-intercept is the point where the graph crosses the y-axis. It occurs when x=0. - To find the y-intercept, we can substitute x=0 into the function.

3. Vertical Asymptote: - A vertical asymptote occurs when the denominator of the function equals zero. - To find the vertical asymptote, we can solve the equation x-3=0.

4. Horizontal Asymptote: - A horizontal asymptote can be found by analyzing the behavior of the function as x approaches positive or negative infinity.

Plotting the Points and Drawing the Graph

Let's start by identifying the key points of the function and then proceed to plot them on the graph.