using the following graph find (approximate when needed)\n(a) the intervals where the function is…

using the following graph find (approximate when needed)\n(a) the intervals where the function is increasing. write the solution in interval notation.\n(b) the intervals where the function is decreasing. write the solution in interval notation.\n(c) the relative minimum.\n(d) the relative maximum.\n(e) the domain and range.

using the following graph find (approximate when needed)\n(a) the intervals where the function is increasing. write the solution in interval notation.\n(b) the intervals where the function is decreasing. write the solution in interval notation.\n(c) the relative minimum.\n(d) the relative maximum.\n(e) the domain and range.

Answer

Explanation:

Step1: Identify increasing intervals

Observe where graph rises. The function is increasing on $(-3,-1)$ and $(1,\infty)$.

Step2: Identify decreasing intervals

Observe where graph falls. The function is decreasing on $(-\infty, - 3)$ and $(-1,1)$.

Step3: Find relative minimum

Locate lowest - point in local regions. The relative minimum is at the point $(1,-3)$.

Step4: Find relative maximum

Locate highest - point in local regions. The relative maximum is at the point $(-1,3)$.

Step5: Find domain and range

Domain is set of all $x$ - values, range is set of all $y$ - values. The domain is $(-\infty,\infty)$ and the range is $[-3,\infty)$.

Answer:

(a) $(-3,-1)\cup(1,\infty)$ (b) $(-\infty,-3)\cup(-1,1)$ (c) $(1,-3)$ (d) $(-1,3)$ (e) Domain: $(-\infty,\infty)$; Range: $[-3,\infty)$