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 $f(x_1)>f(x_2)$. Graphically, the function is decreasing when the graph is going down - hill from left to right.
Step2: Analyze the given graph
By observing the graph of the function $y = f(x)$:
- In the interval $[-2.5,-2]$, the function is increasing (going uphill from left - to - right).
- In the interval $[-2,-1.5]$, the function is decreasing (going downhill from left - to - right).
- In the interval $[-1,1]$, the function is increasing first and then decreasing.
- In the interval $[1.5,2]$, the function is decreasing (going downhill from left - to - right).
- In the interval $[2,2.5]$, the function is increasing (going uphill from left - to - right).
- In the interval $(2.5,3]$, the function is increasing (going uphill from left - to - right).
Answer:
[-2,-1.5], [1.5,2]