Question

use the graph to determine
(a) open intervals on which the
function is increasing, if any.
(b) open intervals on which the
function is decreasing, if any.
(c) open intervals on which the
function is constant, if any.
a. the function is increasing on the interval(s) $(-\infty,-4),(-3,-2)$.
(type your answer in interval notation. use a comma to separate answers as needed.)
b. the function is never increasing.
(b) select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the function is decreasing on the interval(s)
(type your answer in interval notation. use a comma to separate answers as needed)
b. the function is never decreasing

Explanation:

Step1: Analyze the graph for increasing intervals

A function is increasing when, as \(x\) increases, \(y\) also increases. Looking at the graph, we can see that the function is increasing on the intervals \((-5,-4)\) and \((-2,-1)\).

Step2: Analyze the graph for decreasing intervals

A function is decreasing when, as \(x\) increases, \(y\) decreases. From the graph, the function is decreasing on the intervals \((-\infty,-5)\), \((-4,-2)\) and \((-1,\infty)\).

Step3: Analyze the graph for constant intervals

A function is constant when, as \(x\) increases, \(y\) remains the same. Looking at the graph, there are no such intervals.

Answer:

(a) The function is increasing on the interval(s) \((-5,-4),(-2,-1)\)
(b) The function is decreasing on the interval(s) \((-\infty,-5),(-4,-2),(-1,\infty)\)
(c) The function is never constant.