multiple answer 16.7 points\nfor which interval(s) is the function decreasing?\n(5, ∞)\n(-8, -2)\n(2…
multiple answer 16.7 points\nfor which interval(s) is the function decreasing?\n(5, ∞)\n(-8, -2)\n(2, 5)\n(-∞, -8)\n(-2, 0)\n(0, 2)
Answer
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<x_2), we have (f(x_1)>f(x_2)). Graphically, the function has a negative - slope (the graph falls from left - to - right).
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))