Question

На одной координатной плоскости построить графики функций у=1/х и у=х. Выяснить, при каких значениях х: графики этих функций пересекаются. Пожалуйста сделайте на фото.

Answer 1

Пересечение графиков в точках (-1,-1) и (1,1)
Во вложении таблицы и графики

Answer 2

Plotting the Functions on a Coordinate Plane

To plot the functions y = 1/x and y = x on a coordinate plane, we can use the following steps:

1. Identify the Key Points: - For the function y = 1/x, the key points are (1, 1), (2, 0.5), (3, 0.33), and so on. - For the function y = x, the key points are (1, 1), (2, 2), (3, 3), and so on.

2. Plot the Points: - Plot these key points on the coordinate plane.

3. Draw the Curves: - Connect the points to form the curves for the functions y = 1/x and y = x.

Intersection of the Functions

To find the values of x at which the graphs of these functions intersect, we need to solve the equation y = 1/x for y = x.

The intersection points occur when the two functions have the same y-value for a given x-value.

Let's solve for the intersection points: - For y = 1/x, y = x - 1/x = x

Solving the above equation will give us the x-values at which the graphs of these functions intersect.

I will now provide a visual representation of the plotted functions and their intersection points.