Question

given a graph of a function
the function graphed above is:
increasing on the interval(s)
decreasing on the interval(s)

Explanation:

Step1: Understand increasing and decreasing functions

A function is increasing on an interval if, as \(x\) increases, \(y\) also increases. A function is decreasing on an interval if, as \(x\) increases, \(y\) decreases.

Step2: Analyze the graph

Looking at the graph, we can see that the function is increasing between \(x = - 0.5\) and \(x = 2\). For \(x<-0.5\) and \(x > 2\), as \(x\) increases, \(y\) decreases.

Answer:

Increasing on the interval \((-0.5,2)\), Decreasing on the interval \((-\infty,-0.5)\cup(2,\infty)\)