Question

determine where ( f(x) ) is increasing and/or decreasing.
7.
8.

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

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
• For the right - hand part of the graph (from \(x=-2\) to \(\infty\)), if we pick two points \(x_1

Answer:

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