which intervals show f(x) decreasing? check all that apply. -2.5, -2 -2, -1.5 -1, 1 1.5, 2 2, 2.5 (2.5, 3
which intervals show f(x) decreasing? check all that apply. -2.5, -2 -2, -1.5 -1, 1 1.5, 2 2, 2.5 (2.5, 3
Answer
Explanation:
Step1: Recall decreasing - function property
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)). Visually, the graph of the function moves down - ward as we move from left to right.
Step2: Analyze the given graph
Looking at the graph of (y = f(x)):
- In the interval ([-2.5,-2]), the graph is moving upward as we move from left to right, so the function is increasing.
- In the interval ([-2,-1.5]), the graph is moving downward as we move from left to right, so the function is decreasing.
- In the interval ([-1,1]), the graph first moves upward and then downward, so it is not decreasing on the entire interval.
- In the interval ([1.5,2]), the graph is moving downward as we move from left to right, so the function is decreasing.
- In the interval ([2,2.5]), the graph is moving upward as we move from left to right, so the function is increasing.
- In the interval ((2.5,3)), the graph is moving upward as we move from left to right, so the function is increasing.
Answer:
B. ([-2,-1.5]), D. ([1.5,2])