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 comm
click on
one\ if applicable.

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval \((a,b)\) if for any two points \(x_1,x_2\in(a,b)\) with \(x_1

Step2: Analyze the given graph

Looking at the graph:

• For the interval \([- 5,-1]\), as \(x\) moves from \(-5\) to \(-1\), the \(y -\)values of the function are getting smaller.
• For the interval \([2,3]\), as \(x\) moves from \(2\) to \(3\), the \(y -\)values of the function are not changing (it's a horizontal line, so it's not strictly decreasing here).
• For the interval \([3,4]\), as \(x\) moves from \(3\) to \(4\), the \(y -\)values of the function are getting smaller.

Answer:

\([-5,-1],[3,4]\)