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

Explanation:

Step1: Recall decreasing - function property

A function $y = f(x)$ is decreasing on an interval if for any two points $x_1,x_2$ in the interval with $x_1<x_2$, we have $f(x_1)>f(x_2)$. Graphically, the function is going down - hill.

Step2: Analyze the given graph

Examine the graph of $y = f(x)$ to identify the intervals where the curve is sloping downwards.

• 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.
• In the interval $[2,2.5]$, as $x$ increases from $2$ to $2.5$, the $y$ - values of the function are decreasing.

Answer:

[-2,-1.5], [1.5,2], [2,2.5]