Which of the following statements is true about the function f(x)= -x-1?

To determine the behavior of the function \( f(x) = -x - 1 \), we can analyze its slope. The function is linear and has a negative slope:

1. The slope of the function is \(-1\), which means it decreases as \( x \) increases.

Based on this, we can evaluate the provided statements:

a. The function is increasing between \( x=0 \) and \( x=2 \):

• False. The function is decreasing in this interval.

b. The function is increasing between \( x=-2 \) and \( x=0 \):

• False. The function is decreasing in this interval.

c. The function is decreasing from \( x=-2 \) and \( x=0 \):

• True. The function is decreasing in this interval.

d. The function is increasing from \( x=1 \) and \( x=3 \):

• False. The function is decreasing in this interval.

Thus, the correct statement is:

c. The function is decreasing from \( x=-2 \) to \( x=0 \).