Question

a) on what interval(s) is the function increasing? enter your answer in interval notation separating each interval with a comma if needed.
b) on what interval(s) is the function decreasing? enter your answer in interval notation separating each interval with a comma if needed.

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_1Looking 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_1The 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) \([0,5],[10,12],[15,20]\)