Question

Постройте график функции у=|х-1|+1

Answer 1

Відповідь на фото,відкрий ;)

Answer 2

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

To graph the function y = |x - 1| + 1, we can start by analyzing the equation. The function consists of two parts: |x - 1| and + 1. Let's break it down:

1. |x - 1|: This part of the function represents the absolute value of (x - 1). The absolute value function returns the distance of a number from zero. In this case, it represents the distance of (x - 1) from zero. When (x - 1) is positive, the absolute value is equal to (x - 1). When (x - 1) is negative, the absolute value is equal to -(x - 1). Therefore, we can rewrite this part as:

- For x ≥ 1: |x - 1| = (x - 1) - For x < 1: |x - 1| = -(x - 1)

2. + 1: This part of the function simply adds 1 to the result of |x - 1|.

Now, let's analyze the behavior of the function for different values of x:

- For x ≥ 1: The function becomes y = (x - 1) + 1 = x. This means that for x values greater than or equal to 1, the graph of the function is a straight line with a slope of 1 and a y-intercept of 0.

- For x < 1: The function becomes y = -(x - 1) + 1 = 2 - x. This means that for x values less than 1, the graph of the function is a straight line with a slope of -1 and a y-intercept of 2.

To summarize, the graph of the function y = |x - 1| + 1 consists of two straight lines intersecting at x = 1. The line for x ≥ 1 has a positive slope of 1 and passes through the origin (0, 0), while the line for x < 1 has a negative slope of -1 and intersects the y-axis at (0, 2).

Let's plot this graph to visualize it.