consider the function in the graph to the right.\nthe function has a maximum of\nat x =\n\nthe function has…

Explanation:

Step1: Identify maximum point

By observing the graph, the highest - point is at $( - 3,8)$. So the function has a maximum of $8$ at $x=-3$.

Step2: Identify minimum point

The lowest - point is at $(1,0)$. So the function has a minimum of $0$ at $x = 1$.

Step3: Determine increasing intervals

The function is increasing when the graph goes up as we move from left to right. The increasing intervals are $(-\infty,-3)$ and $(1,\infty)$.

Step4: Determine decreasing intervals

The function is decreasing when the graph goes down as we move from left to right. The decreasing interval is $(-3,1)$.

Step5: Find the domain

The domain is the set of all possible $x$ - values. Since the graph extends infinitely to the left and right, the domain is $(-\infty,\infty)$.

Step6: Find the range

The range is the set of all possible $y$ - values. The lowest $y$ - value is $0$ and it extends infinitely up, so the range is $[0,\infty)$.

Answer:

The function has a maximum of $8$ at $x=-3$. The function has a minimum of $0$ at $x = 1$. The function is increasing on the intervals $(-\infty,-3)$ and $(1,\infty)$. The function is decreasing on the interval $(-3,1)$. The domain of the function is $(-\infty,\infty)$. The range of the function is $[0,\infty)$.