Question

identify the intervals where the graph is increasing, decreasing and constant.
increasing on the interval(s)
decreasing on the interval(s)
constant on the interval(s)
question help: video message instructor

Explanation:

Step1: Recall the definitions

• A function is increasing if as \(x\) increases, \(y\) increases.
• A function is decreasing if as \(x\) increases, \(y\) decreases.
• A function is constant if as \(x\) increases, \(y\) remains the same.

Step2: Analyze the graph

• Looking at the graph, we can see that the function is decreasing from \(x = -\infty\) to \(x=-4\).
• The function is constant from \(x=-4\) to \(x = 2\).
• The function is increasing from \(x = 2\) to \(x=\infty\).

Answer:

• Increasing on the interval \((2,\infty)\)
• Decreasing on the interval \((-\infty,-4)\)
• Constant on the interval \((-4,2)\)