Question

essay 4 points for the graph below, list where the function is increasing and where the function is decreasing.

Explanation:

Step1: Understand increasing and decreasing

A function is increasing when, as \(x\) increases, \(y\) also increases. A function is decreasing when, as \(x\) increases, \(y\) decreases.

Step2: Analyze the graph

Looking at the graph:

• From \(x =-\infty\) to \(x=-5\), as \(x\) increases, \(y\) decreases.
• From \(x=-5\) to \(x = - 3\), as \(x\) increases, \(y\) increases.
• From \(x=-3\) to \(x=1\), as \(x\) increases, \(y\) decreases.
• From \(x = 1\) to \(x=\infty\), as \(x\) increases, \(y\) increases.

Answer:

The function is increasing on the intervals \((-\infty,-5)\) and \((1,\infty)\). The function is decreasing on the intervals \((-5,-3)\) and \((-3,1)\).