determine the intervals on which the function is increasing, decreasing, and constant. list the interval(s)…

determine the intervals on which the function is increasing, decreasing, and constant. list the interval(s) on which the function is increasing. (-∞,-7),(-2,-1) (type your answer in interval notation. use a comma to separate answers as needed.) list the interval(s) on which the function is decreasing. (-7,-5) (type your answer in interval notation. use a comma to separate answers as needed.) list the interval(s) on which the function is constant. (type your answer in interval notation. use a comma to separate answers as needed.)

determine the intervals on which the function is increasing, decreasing, and constant. list the interval(s) on which the function is increasing. (-∞,-7),(-2,-1) (type your answer in interval notation. use a comma to separate answers as needed.) list the interval(s) on which the function is decreasing. (-7,-5) (type your answer in interval notation. use a comma to separate answers as needed.) list the interval(s) on which the function is constant. (type your answer in interval notation. use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Recall function behavior definitions

A function is increasing when the y - values increase as the x - values increase, decreasing when y - values decrease as x - values increase, and constant when y - values do not change as x - values change.

Step2: Analyze the graph

By observing the graph, we see that the function goes up (is increasing) for (x\in(-\infty,-7)) and (x\in(-2, - 1]). It goes down (is decreasing) for (x\in(-7,-5)). And for the constant part, we look for horizontal segments. We can see the function is constant for (x\in[-5,-2]) and (x\in[1,\infty)).

Answer:

Increasing intervals: ((-\infty,-7),(-2, - 1]) Decreasing intervals: ((-7,-5)) Constant intervals: ([-5,-2],[1,\infty))