Question

answer
attempt 2 out of 2
the function is decreasing on the interval -8 < x < -2 (segment 1),
increasing on the interval -2 < x < 1 (segment 2), and decreasing on the
interval 7 < x < -8 (segment 3).

Explanation:

Step1: Understand increasing and decreasing functions

A function is decreasing if as \(x\) increases, \(y\) decreases. A function is increasing if as \(x\) increases, \(y\) increases.

Step2: Analyze each segment

• Segment 1 (\(-8 < x < - 2\)): As \(x\) increases (moves from left to right on the \(x\) - axis in the interval \(-8 < x < -2\)), \(y\) (the value of the function) decreases.
• Segment 2 (\(-2 < x < 1\)): As \(x\) increases (moves from left to right on the \(x\) - axis in the interval \(-2 < x < 1\)), \(y\) (the value of the function) decreases.
• Segment 3 (\(1 < x < 7\)): As \(x\) increases (moves from left to right on the \(x\) - axis in the interval \(1 < x < 7\)), \(y\) (the value of the function) increases.

Answer:

The function is decreasing on the interval \(-8 < x < -2\), decreasing on the interval \(-2 < x < 1\), and increasing on the interval \(1 < x < 7\).