Question

determine the interval(s) on which the function is (strictly) decreasing. write your answer as an interval or list of intervals. when writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible. click on
one\ if applicable.

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is strictly decreasing on an interval \((a,b)\) if for any \(x_1,x_2\in(a,b)\) with \(x_1 < x_2\), we have \(f(x_1)>f(x_2)\).

Step2: Analyze the graph

Looking at the graph, we observe the part of the function where as \(x\) increases (moves from left - to - right), \(y\) (the value of the function) decreases.
We check the \(x\) - values for this behavior. The \(x\) - values for which the function is decreasing start at \(x=-2\) (not included, because the function changes its behavior at a point, and we consider open intervals for strict monotonicity in most cases for non - differentiable points in the context of basic calculus - like graph analysis) and end at \(x = - 1\) (not included).

So the interval on which the function is strictly decreasing is \((-2,-1)\).

Answer:

$(-2,-1)$