Question

-1/x график функции, при каких значениях х функция принимает положительные и при каких отрицательные значения

Answer 1

Если x>0, то функция принимает отрицательное значение, есиже х<0, функция принимает положительное положение

Answer 2

To understand when the function f(x) = -1/x takes positive or negative values, we need to consider the sign of f(x) for different values of x. Remember that the sign of a number is positive if it's greater than zero, negative if it's less than zero, and zero if the number itself is zero.

1. When x > 0: For positive values of x, -1/x will be negative. As x gets larger, the absolute value of -1/x approaches zero, but it is always negative. For example: -1/1 = -1 -1/2 = -0.5 -1/10 = -0.1 As x approaches zero from the right, -1/x approaches negative infinity.

2. When x < 0: For negative values of x, -1/x will be positive. As x becomes more negative, the absolute value of -1/x increases. For example: -1/(-1) = 1 -1/(-2) = 0.5 -1/(-10) = 0.1 As x approaches zero from the left, -1/x approaches positive infinity.

3. At x = 0: The function -1/x is undefined at x = 0 because division by zero is not allowed.

In summary:

• For x > 0, the function f(x) = -1/x takes negative values.
• For x < 0, the function f(x) = -1/x takes positive values.
• The function is undefined at x = 0.

Keep in mind that -1/x is a continuous function, meaning there are no breaks or jumps in its graph except for the vertical asymptote at x = 0 where the function approaches infinity from both sides but does not have a defined value.