Question

for which interval(s) is the function decreasing?
(-\infty,-8)
(-8,-2)
(0,2)
(2,5)
(5,\infty)
(-2,0)

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze each interval

• Interval \((-\infty,-8)\):

The graph is decreasing on \((-\infty,-8)\) because as \(x\) increases (moves from left to right) in this interval, \(y\) decreases.

• Interval \((-8,-2)\):

The graph is increasing on \((-8,-2)\) because as \(x\) increases (moves from left to right) in this interval, \(y\) increases.

• Interval \((0,2)\):

The graph is increasing on \((0,2)\) because as \(x\) increases (moves from left to right) in this interval, \(y\) increases.

• Interval \((2,5)\):

The graph is decreasing on \((2,5)\) because as \(x\) increases (moves from left to right) in this interval, \(y\) decreases.

• Interval \((5,\infty)\):

The graph is increasing on \((5,\infty)\) because as \(x\) increases (moves from left to right) in this interval, \(y\) increases.

• Interval \((-2,0)\):

The graph is decreasing on \((-2,0)\) because as \(x\) increases (moves from left to right) in this interval, \(y\) decreases.

Answer:

\((-\infty,-8)\), \((-2,0)\), \((2,5)\)