Question

score: 0 of 1 point
identify the intervals where the graph is increasing and decreasing. if there is more
than one interval, use a union ∪ to combine them.
(graph with x-axis from -5 to 5 and y-axis from -5 to 5, showing a curve)

Explanation:

Step1: Recall the definition of increasing and decreasing functions

A function \(y = f(x)\) is increasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the graph

Looking at the graph:

• For the interval \((-\infty,-3)\), as \(x\) increases (moves from left - to - right), \(y = f(x)\) increases.
• For the interval \((-3,-1)\), as \(x\) increases (moves from left - to - right), \(y = f(x)\) decreases.
• For the interval \((-1,\infty)\), as \(x\) increases (moves from left - to - right), \(y = f(x)\) increases.

Answer:

The function is increasing on the intervals \((-\infty,-3)\cup(-1,\infty)\) and decreasing on the interval \((-3,-1)\).