determine where ( f(x) ) is increasing and/or decreasing.\n7.\n8.

Explanation:

Step1: Recall the definition of increasing and decreasing functions

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)). A function is decreasing 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)).

Step2: Analyze the graph

Looking at the graph, we can see that as (x) moves from (-\infty) to a certain point (let's say (x = a)), the (y)-values of the function are getting smaller. Then, as (x) moves from (x=a) to (\infty), the (y)-values of the function are also getting smaller. But wait, actually, if we consider the slope - concept (a non - calculus way, for a graph, if we move from left to right):

• For the left - hand part of the graph (from (-\infty) to some (x) - value, say (x=-2) approximately), if we pick two points (x_1<x_2) in the interval ((-\infty, - 2)), (f(x_1)>f(x_2)) (the function is going down as we move from left to right).
• For the right - hand part of the graph (from (x=-2) to (\infty)), if we pick two points (x_1<x_2) in the interval ((-2,\infty)), (f(x_1)>f(x_2)) (the function is going down as we move from left to right).

Answer:

The function (f(x)) is decreasing on the interval ((-\infty,\infty)).