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
Answer
Explanation:
Step1: Recall decreasing - function definition
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)). In a graph, the function is decreasing when the graph moves down - ward as we move from left to right.
Step2: Analyze the graph for each interval
- For the interval ([-2.5,-2]): As we move from (x=-2.5) to (x = - 2) on the (x) - axis, the (y) - values of the function are decreasing.
- For the interval ([-2,-1.5]): As we move from (x=-2) to (x=-1.5), the (y) - values of the function are increasing.
- For the interval ([-1,1)): As we move from (x = - 1) to (x = 1), the (y) - values of the function first increase and then decrease.
- For the interval ([1.5,2]): As we move from (x = 1.5) to (x = 2), the (y) - values of the function are decreasing.
- For the interval ([2,2.5)): As we move from (x = 2) to (x = 2.5), the (y) - values of the function are increasing.
- For the interval ((2.5,3]): As we move from (x = 2.5) to (x = 3), the (y) - values of the function are increasing.
Answer:
[-2.5,-2], [1.5,2]