determine all intervals on which the graph of ( f ) is decreasing.
determine all intervals on which the graph of ( f ) is decreasing.
Answer
Explanation:
Step1: Recall the definition of a 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)). Graphically, this means the function's graph moves down - ward as (x) increases.
Step2: Analyze the given graph
Looking at the graph of (y = f(x)):
- For the interval ((-\infty,-3)), as (x) increases (moves from left to right), the (y) - values of the function first decrease (from the left - hand side of the graph towards (x=-7)) and then increase towards (x = - 3).
- For the interval ((-1,2)), as (x) increases from (-1) to (2), the (y) - values of the function decrease.
- For the other intervals (((-3,-1)) the function is increasing, ((2,\infty)) the function is increasing)
Answer:
((-1,2))