identifying intervals on which a function is decreasing\nwhich intervals show f(x) decreasing? check all…

identifying intervals on which a function is decreasing\nwhich intervals show f(x) decreasing? check all that apply.\n-2.5, -2\n-2, -1.5\n-1, 1\n1.5, 2\n2, 2.5\n(2.5, 3

identifying intervals on which a function is decreasing\nwhich intervals show f(x) decreasing? check all that apply.\n-2.5, -2\n-2, -1.5\n-1, 1\n1.5, 2\n2, 2.5\n(2.5, 3

Answer

Answer:

  • [-2,-1.5]
  • [1.5,2]

Explanation:

Step1: Recall decreasing - function concept

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)).

Step2: Analyze the graph

Looking at the graph of (y = f(x)), we observe the slope of the curve. When the curve is going down - hill (from left to right), the function is decreasing. In the interval ([-2,-1.5]), as (x) increases from (- 2) to (-1.5), the (y) - values of the function are decreasing. In the interval ([1.5,2]), as (x) increases from (1.5) to (2), the (y) - values of the function are decreasing. For ([-2.5,-2]), the function is increasing. For ([-1,1]), the function first increases and then decreases. For ([2,2.5]) and ((2.5,3]), the function is increasing.