(a) find the open intervals on which the function shown in the graph is increasing and decreasing. (b)…

(a) find the open intervals on which the function shown in the graph is increasing and decreasing. (b) identify the functions local and absolute extreme values, if any, saying where they occur. (a) on what open interval(s), if any, is the function increasing? select the correct choice below and fill in any answer boxes within your choice. a. the function is increasing on the open interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never increasing. on what open interval(s), if any, is the function decreasing? select the correct choice below and fill in any answer boxes within your choice. a. the function is decreasing on the open interval(s) (type your answer in interval notation. use a comma to separate answers as needed.)

(a) find the open intervals on which the function shown in the graph is increasing and decreasing. (b) identify the functions local and absolute extreme values, if any, saying where they occur. (a) on what open interval(s), if any, is the function increasing? select the correct choice below and fill in any answer boxes within your choice. a. the function is increasing on the open interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never increasing. on what open interval(s), if any, is the function decreasing? select the correct choice below and fill in any answer boxes within your choice. a. the function is decreasing on the open interval(s) (type your answer in interval notation. use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Analyze increasing intervals

A function is increasing when the graph rises from left - to - right. From the graph, we can see that the function is increasing on the intervals $(-8,-4)$ and $(0,2)$.

Step2: Analyze decreasing intervals

A function is decreasing when the graph falls from left - to - right. The function is decreasing on the intervals $(-4,0)$ and $(2,8)$.

Step3: Identify local extreme values

Local maxima occur where the function changes from increasing to decreasing. Local minima occur where the function changes from decreasing to increasing. Local maximum values are $y = 6$ at $x=-4$ and $y = 2$ at $x = 2$. Local minimum value is $y=-2$ at $x = 0$.

Step4: Identify absolute extreme values

The absolute maximum value is the highest $y$ - value of the function. Here, the absolute maximum is $y = 6$ at $x=-4$. The absolute minimum value is the lowest $y$ - value of the function. Here, the absolute minimum is $y=-4$ at $x = 8$.

Answer:

(a) A. The function is increasing on the open intervals $(-8,-4),(0,2)$. A. The function is decreasing on the open intervals $(-4,0),(2,8)$. (b) Local maximum values: $y = 6$ at $x=-4$, $y = 2$ at $x = 2$. Local minimum value: $y=-2$ at $x = 0$. Absolute maximum value: $y = 6$ at $x=-4$. Absolute minimum value: $y=-4$ at $x = 8$.