determine all intervals on which the graph of f is increasing.
determine all intervals on which the graph of f is increasing.
Answer
Explanation:
Step1: Recall increasing - graph property
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)). Graphically, the function is increasing when the slope of the tangent line is positive, or the graph is rising from left - to - right.
Step2: Analyze the given graph
Looking at the graph of (y = f(x)), we observe the intervals where the graph is rising. We can see that the graph is rising from (x=-9) to (x = - 4) and from (x=2) to (x=8).
Answer:
((-9,-4)\cup(2,8))