Question

score on last try: 0 of 1 pts. see details for more.
at least one scored part is incorrect. jump to first changable incorrect part.

next question you can retry this question below

the function graphed above is:
increasing on the interval(s)
decreasing on the interval(s)
submit question

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, we find the critical points (where the slope of the tangent line is zero). The function has a local minimum at \(x=-1\) and a local maximum at \(x = 3\).

• For the increasing interval:

We observe that as \(x\) moves from \(-1\) to \(3\), the \(y\) - values of the function are increasing. So the increasing interval is \((-1,3)\)

• For the decreasing interval:

As \(x\) moves from \(-\infty\) to \(-1\) (left - hand side of \(x = - 1\)), the \(y\) - values of the function are decreasing. Also, as \(x\) moves from \(3\) to \(\infty\) (right - hand side of \(x = 3\)), the \(y\) - values of the function are decreasing. So the decreasing intervals are \((-\infty,-1)\cup(3,\infty)\)

Answer:

Increasing on the interval(s): \((-1,3)\)
Decreasing on the interval(s): \((-\infty,-1)\cup(3,\infty)\)