Question

Question

Consider the given function.

Where is this function decreasing?

Enter your answer by filling in the boxes.

The function is decreasing from x =
to x =
.
A segment extends from negative 5 comma 0 to negative 2 comma 5. A segment extends from negative 2 comma 5 to 1 comma 5. A segment extends from 1 comma 5 to 8 comma negative 2.

Answer 1

To determine where the function is decreasing, we should analyze the segments you've described based on their endpoints.

1. The segment from (-5, 0) to (-2, 5):

   • The y-values go from 0 to 5, which means the function is increasing here.

2. The segment from (-2, 5) to (1, 5):

   • The y-values remain constant at 5, so the function is constant here.

3. The segment from (1, 5) to (8, -2):

   • The y-values go from 5 down to -2, which means the function is decreasing here.

Based on this analysis, the function is decreasing from \( x = 1 \) to \( x = 8 \).

Thus, the final answer is:

The function is decreasing from x = 1 to x = 8.