Question

multiple answer 16.7 points
for which interval(s) is the function decreasing?
(5, ∞)
(-8, -2)
(2, 5)
(-∞, -8)
(-2, 0)
(0, 2)

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

• For the interval \((-\infty,-8)\):

As \(x\) increases (moves from left - to - right) in the interval \((-\infty,-8)\), the \(y\) - values of the function increase. So the function is increasing on \((-\infty,-8)\).

• For the interval \((-8,-2)\):

As \(x\) moves from \(-8\) to \(-2\) (left - to - right), the \(y\) - values of the function increase (from \(y = - 4\) to \(y = 6\)). So the function is increasing on \((-8,-2)\).

• For the interval \((-2,0)\):

As \(x\) moves from \(-2\) to \(0\) (left - to - right), the \(y\) - values of the function decrease (from \(y = 6\) to \(y = 0\)).

• For the interval \((0,2)\):

As \(x\) moves from \(0\) to \(2\) (left - to - right), the \(y\) - values of the function increase (from \(y = 0\) to \(y = 10\)). So the function is increasing on \((0,2)\).

• For the interval \((2,5)\):

As \(x\) moves from \(2\) to \(5\) (left - to - right), the \(y\) - values of the function decrease (from \(y = 10\) to \(y = 0\)).

• For the interval \((5,\infty)\):

As \(x\) moves from \(5\) to \(\infty\) (left - to - right), the \(y\) - values of the function increase. So the function is increasing on \((5,\infty)\).

Answer:

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