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

Question

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 analyze the function \( f(x) = -x - 1 \), we can look at its derivative to determine whether it is increasing or decreasing:

1. Calculate the derivative: \[ f'(x) = -1 \] The derivative \( f'(x) = -1 \) is negative for all \( x \), which indicates that the function is decreasing everywhere on its domain.

2. Evaluate the given statements:

   • a. The function is increasing between \( x=0 \) and \( x=2 \): False (the function is decreasing).
   • b. The function is increasing between \( x=-2 \) and \( x=0 \): False (the function is decreasing).
   • c. The function is decreasing from \( x=-2 \) to \( x=0 \): True (the function is always decreasing).
   • d. The function is increasing from \( x=1 \) to \( x=3 \): False (the function is decreasing).

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