the function f is graphed below. determine the intervals on which f is increasing and decreasing.
the function f is graphed below. determine the intervals on which f is increasing and decreasing.
Answer
Explanation:
Step1: Recall increasing - decreasing function rules
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), (f(x_1)<f(x_2)), and decreasing if (f(x_1)>f(x_2)).
Step2: Analyze the graph
Looking at the graph, from left - to - right, the function is increasing when the graph goes up. We can see that the function (y = f(x)) is increasing on the interval ([- 3,2]) because as (x) increases from (-3) to (2), the (y) - values of the function are getting larger.
Step3: Continue analyzing the graph
The function is decreasing on the interval ([2,5]) since as (x) increases from (2) to (5), the (y) - values of the function are getting smaller. And it is increasing again on the interval ([5,9]) as (x) increases from (5) to (9), the (y) - values of the function are getting larger.
Answer:
The function (f(x)) is increasing on the intervals ([-3,2]) and ([5,9]), and decreasing on the interval ([2,5]).