Question

График У= - Х+3 Вопрос: Найти точку пересечения графика с осями координат и выяснить возрастает или убывает заданная функция. Подробно объяснить, если можно!

Answer 1

Y=-x+3 ⇒y=kx+b⇒k=-1;b=3
функция убывает при всех x,так как k<0;
x=0 ⇒y=3;⇒точка пересечения с осью абсцисс;
y=0 ⇒x=3; ⇒точка пересечения с осью ординат

Answer 2

Finding the Intersection Point and Determining the Function's Behavior

To find the intersection point of the graph and determine whether the given function is increasing or decreasing, we can start by analyzing the function U = -X + 3.

The intersection points with the coordinate axes can be found by setting each axis coordinate to zero and solving for the other variable. This will give us the points where the graph intersects the x-axis and the y-axis.

1. Intersection with the x-axis (U = 0): - To find the point of intersection with the x-axis, we set U (or Y) to 0 and solve for X. - The point of intersection with the x-axis is at (3, 0).

2. Intersection with the y-axis (X = 0): - Setting X to 0 and solving for U (or Y) gives us the point of intersection with the y-axis. - The point of intersection with the y-axis is at (0, 3).

Now, let's determine whether the function is increasing or decreasing.

The given function is U = -X + 3. This is a linear function in the form of U = kX + b, where k is the slope and b is the y-intercept.

The slope of the function is -1. Since the slope is negative, the function is decreasing. This means that as X increases, U decreases, and vice versa.

In summary, the graph of the function U = -X + 3 intersects the x-axis at (3, 0) and the y-axis at (0, 3). The function is decreasing.

I hope this helps! If you have any further questions or need additional clarification, feel free to ask.