Question

score: 0 of 1 point
given a graph of a function
the function graphed above is:
increasing on the interval(s)
enter your answer
decreasing on the interval(s)
enter your answer

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, as \(x\) moves from \(-\infty\) to \(3\), we observe the behavior of the \(y -\)values.

• For the increasing interval:

We see that as \(x\) increases from \(-1\) to \(3\), the \(y -\)values of the function increase. So the function is increasing on the interval \((-1,3)\)

• For the decreasing interval:

As \(x\) increases from \(-\infty\) to \(-1\), the \(y -\)values of the function decrease. So the function is decreasing on the interval \((-\infty,-1)\)

Answer:

Increasing on \((-1,3)\); Decreasing on \((-\infty,-1)\)