Question

9. Побудуйте графік функції y = |x - 1| - 2

Answer 1

ответ:

всегда рад помочь

Answer 2

Plot of the Function y = |x - 1| + 2

To plot the function y = |x - 1| + 2, we can start by understanding the behavior of the absolute value function. The absolute value function returns the distance of a number from zero, regardless of its sign. In this case, the expression |x - 1| represents the distance of x from 1.

Let's break down the function into two cases:

1. When x is greater than or equal to 1: - In this case, the expression |x - 1| simplifies to (x - 1) since x is already greater than or equal to 1. - Therefore, the function becomes y = (x - 1) + 2, which simplifies to y = x + 1.

2. When x is less than 1: - In this case, the expression |x - 1| simplifies to -(x - 1) since x is less than 1. - Therefore, the function becomes y = -(x - 1) + 2, which simplifies to y = -x + 3.

Now, let's plot the graph of the function y = |x - 1| + 2:


The graph consists of two linear segments. The first segment is y = x + 1, which starts from the point (1, 2) and continues as a straight line with a slope of 1. The second segment is y = -x + 3, which starts from the point (1, 2) and continues as a straight line with a slope of -1.

Please note that the graph is a visual representation of the function and can help us understand its behavior and key points, such as the intercepts and slopes.