for which interval(s) is the function decreasing?\n(-\\infty,-8)\n(-8,-2)\n(0,2)\n(2,5)\n(5,\\infty)\n(-2,0)
for which interval(s) is the function decreasing?\n(-\\infty,-8)\n(-8,-2)\n(0,2)\n(2,5)\n(5,\\infty)\n(-2,0)
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 goes down from left - to - right).
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))