Question

the function graphed above is: increasing on the interval(s) decreasing on the interval(s)

Explanation:

Step1: Recall increasing - decreasing function definition

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 of the function, we see that the function is moving upwards (increasing) when \(x\) is in the intervals \((-2, - 1)\) and \((2,4)\).

Step3: Determine decreasing intervals

The function is moving downwards (decreasing) when \(x\) is in the intervals \((-5,-2)\) and \((-1,2)\).

Answer:

Increasing on the interval(s): \((-2,-1)\cup(2,4)\)
Decreasing on the interval(s): \((-5,-2)\cup(-1,2)\)