Question

Постройте график уравнения y+|y|=x

Answer 1

Модуль из у выглядит как парабола, только перевернутая и половинка ее

Answer 2

Graph of the Equation y = |y| = x

To graph the equation y = |y| = x, we need to understand the properties of the absolute value function. The absolute value function returns the distance of a number from zero on the number line. It always returns a non-negative value.

The equation y = |y| = x can be rewritten as two separate equations: 1. y = |y| 2. |y| = x

Let's analyze each equation separately.

Equation 1: y = |y|

In this equation, y is equal to its absolute value. This means that y can be either positive or zero. When y is positive, it remains the same. When y is zero, it also remains the same.

Equation 2: |y| = x

In this equation, the absolute value of y is equal to x. This means that y can be either positive or negative. When y is positive, it is equal to x. When y is negative, it is equal to the negation of x.

Now, let's combine the information from both equations to graph the equation y = |y| = x.

Graphing the Equation

To graph the equation y = |y| = x, we can plot a few points and connect them to form the graph.

1. When y is positive, it remains the same. So, for y = 1, the equation becomes 1 = |1| = 1, which is true. Therefore, the point (1, 1) is on the graph. 2. When y is zero, it remains the same. So, for y = 0, the equation becomes 0 = |0| = 0, which is true. Therefore, the point (0, 0) is on the graph. 3. When y is negative, it is equal to the negation of x. So, for y = -1, the equation becomes |-1| = -1, which is false. Therefore, the point (-1, -1) is not on the graph.

Based on these points, we can plot the graph of the equation y = |y| = x. It consists of two lines: one passing through the points (1, 1) and (0, 0), and another passing through the point (-1, -1).

Please note that the graph of the equation y = |y| = x is not a function because it fails the vertical line test. It is a set of points that satisfy the equation.


Note: The graph provided is a rough sketch and may not be to scale. It is always recommended to use graphing software or a graphing calculator for accurate representations of equations.