Question

Построить график функции |x| + |y| = 1

Answer 1

X>=0 y>=0 x+y=1  y=1-x
x>=0 y<0 x-y=1  y=x-1
x<0 y>=0 -x+y=1  y=1+x
x<0 y<0 -x-y=1  y=-1-x

Answer 2

Graph of the Function |x| + |y| = 1

To graph the function |x| + |y| = 1, we need to understand the properties of absolute value functions. The absolute value of a number is its distance from zero on the number line. The absolute value function |x| takes any real number x and returns its non-negative value.

The equation |x| + |y| = 1 represents a geometric shape known as a diamond or a rhombus. It consists of four line segments that connect the points where the absolute values of x and y are equal to 1.

To graph the function, we can consider different cases based on the signs of x and y:

1. When both x and y are positive: - In this case, the equation |x| + |y| = 1 simplifies to x + y = 1. - The graph of this equation is a line segment connecting the points (1, 0) and (0, 1).

2. When x is positive and y is negative: - In this case, the equation |x| + |y| = 1 simplifies to x - y = 1. - The graph of this equation is a line segment connecting the points (1, 2) and (0, -1).

3. When x is negative and y is positive: - In this case, the equation |x| + |y| = 1 simplifies to -x + y = 1. - The graph of this equation is a line segment connecting the points (-1, 2) and (0, 1).

4. When both x and y are negative: - In this case, the equation |x| + |y| = 1 simplifies to -x - y = 1. - The graph of this equation is a line segment connecting the points (-1, 0) and (0, -1).

By combining all these line segments, we obtain the graph of the function |x| + |y| = 1, which is a diamond shape centered at the origin.

Here is the graph of the function:


Please note that the graph is symmetric with respect to the x-axis and the y-axis.

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