Question

homework assignment 3.3 rates of change and behavior of graphs score: 6/11 answered: 7/11 question 9 consider the function graphed at right. the function has a maximum of 1 at x = the function is increasing on the interval(s): the function is decreasing on the interval(s): question help: video written example message instructor submit question

Explanation:

Step1: Locate maximum point

By observing the graph, the peak of the function is at the point where the $y -$ value is highest. The maximum value of the function shown is $y = 4$ (not $1$ as wrongly filled in the question), and it occurs at $x = 2$.

Step2: Determine increasing interval

A function is increasing when the $y -$ values are getting larger as $x$ increases. From the graph, the function is increasing on the interval $(-1,2)$.

Step3: Determine decreasing interval

A function is decreasing when the $y -$ values are getting smaller as $x$ increases. From the graph, the function is decreasing on the intervals $(-\infty,-1)$ and $(2,\infty)$.

Answer:

The function has a maximum of $4$ at $x = 2$.
The function is increasing on the interval $(-1,2)$.
The function is decreasing on the intervals $(-\infty,-1)$ and $(2,\infty)$.