Question

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

a.
The function is increasing between x=0 and x=2

b.
The function is increasing between x=-2 and x=0

c.
The function is decreasing from x=-2 and x=0.

d.
The function is increasing from x=1 and x=3

Answer 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 \( x=0 \).**