a) on what interval(s) is the function increasing? enter your answer in interval notation separating each…

Explanation:

Step1: Recall the definition of increasing function

A function (y = f(x)) is increasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)<f(x_2)). Visually, the graph of an increasing function rises from left - to - right. Looking at the given graph, we can see that the function is increasing in the intervals where the slope of the line segments is positive. The function is increasing in the interval ([5,10]) (because as (x) moves from (5) to (10), (y) increases from (7) to (11)) and ([12,15]) (because as (x) moves from (12) to (15), (y) increases from (3) to (5))

Step2: Recall the definition of decreasing function

A function (y = f(x)) is decreasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)>f(x_2)). Visually, the graph of a decreasing function falls from left - to - right. The function is decreasing in the interval ([0,5]) (because as (x) moves from (0) to (5), (y) decreases from (20) to (7)), ([10,12]) (because as (x) moves from (10) to (12), (y) decreases from (11) to (3)) and ([15,20]) (because as (x) moves from (15) to (20), (y) decreases from (5) to (0))

Answer:

a) ([5,10],[12,15]) b) ([0,5],[10,12],[15,20])