homework assignment 3.3 rates of change and behavior of graphs score: 6/11 answered: 7/11 question 9…
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
Answer
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 $(2,\infty)$.