Question

the function graphed above is: increasing on the interval(s) decreasing on the interval(s) question help: video message instructor

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:

• The function is increasing on the interval \((-2,2)\) because as \(x\) moves from \(-2\) to \(2\), the \(y\) - values of the function get larger.
• The function is decreasing on the intervals \((-\infty,-2)\) and \((2,\infty)\) because as \(x\) moves from \(-\infty\) to \(-2\) (left - to - right), the \(y\) - values of the function get smaller and as \(x\) moves from \(2\) to \(\infty\) (left - to - right), the \(y\) - values of the function get smaller.

Answer:

Increasing on the interval(s): \((-2,2)\)
Decreasing on the interval(s): \((-\infty,-2)\cup(2,\infty)\)