list the interval(s) on which f is increasing. the interval(s) on which f is increasing is/are (type your…

list the interval(s) on which f is increasing. the interval(s) on which f is increasing is/are (type your answer in interval notation. use a comma to separate answers as needed)

list the interval(s) on which f is increasing. the interval(s) on which f is increasing is/are (type your answer in interval notation. use a comma to separate answers as needed)

Answer

Explanation:

Step1: Recall the definition of an increasing function

A function (y = f(x)) is increasing 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, this means the function rises as we move from left - to - right.

Step2: Analyze the graph

Looking at the graph:

  • From (x=-4) to (x = - 2), the function is decreasing (it goes down as we move from left - to - right).
  • From (x=-2) to (x = 1), the function is increasing (it goes up as we move from left - to - right).
  • From (x = 1) to (x=2), the function is decreasing.
  • From (x = 2) to (x=4), the function is increasing.

Answer:

((-2,1),(2,4))