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

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 $f(x_1)>f(x_2)$. Graphically, the function is going down - hill from left to right.

Step2: Analyze the given graph

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

  • 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.

Answer:

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