F(x)=|x-2|+|x|+|x+2|

Предыдущий
вопрос Следующий
вопрос

This function can be broken up into different cases depending on the value of x:

Case 1: x < -2

When x < -2, all three absolute values will be negative. So we have:
F(x) = -(x-2) - x - (x+2) = -x +2 - x - x - 2 = -3x

Case 2: -2 ≤ x < 0

When -2 ≤ x < 0, the absolute values |x| and |x+2| will be negative, while |x-2| will be positive. So we have:
F(x) = (x-2) - x - (x+2) = x - 2 - x - x - 2 = -2x - 4

Case 3: 0 ≤ x < 2

When 0 ≤ x < 2, the absolute values |x-2| and |x+2| will be negative, while |x| will be positive. So we have:
F(x) = (x-2) + x - (x+2) = x - 2 + x - x - 2 = -2

Case 4: x ≥ 2

When x ≥ 2, all three absolute values will be positive. So we have:
F(x) = (x-2) + x + (x+2) = x - 2 + x + x + 2 = 3x

Putting it all together, the function F(x) = |x-2|+|x|+|x+2| can be written as:
F(x) =
-3x for x < -2
-2x - 4 for -2 ≤ x < 0
-2 for 0 ≤ x < 2
3x for x ≥ 2