Question

For the function f(x) = -1x, x<0; please judge its changing in the domain.

A. It is always increasing.
B. It is always decreasing.
C. It is partly increasing, partly decreasing.
D. None of the above.

Answer 1

The function f(x) = -1x for x<0 is a straight line with a negative slope and is always decreasing in the domain where x is less than 0.

Step-by-step explanation:

The function in question is f(x) = -1x for the domain where x is less than 0 (x<0). To judge its change, we need to analyze the slope of the function. Since the function is described by a straight line with a negative slope, it means that as x decreases (moves leftward on the number line, where x is already negative), the value of f(x) decreases as well. Thus, for the domain given (x<0), the function is consistently decreasing as x becomes more negative. Therefore, the correct answer to the question is B. It is always decreasing.