Question

find the open interval(s) where the following function is increasing, decreasing, or constant. express your answer in interval notation. answer selecting an option will display any text boxes needed to complete your answer. increasing on one interval decreasing on one interval constant on one interval increasing on one interval and decreasing on another

Explanation:

Step1: Analyze the function's graph

For a function \(y = f(x)\), if as \(x\) increases, \(y\) also increases, the function is increasing. If as \(x\) increases, \(y\) decreases, the function is decreasing.
Looking at the graph, we can observe the following:

• Let's assume the vertex of the parabola (the lowest point of the U - shaped graph) has an \(x\) - coordinate \(x = - 2\) (by visual inspection of the grid).
• For \(x<-2\) (i.e., in the interval \((-\infty,-2)\)), as \(x\) increases (moving from left to right on the \(x\) - axis), the \(y\) - values of the function decrease.
• For \(x > - 2\) (i.e., in the interval \((-2,\infty)\)), as \(x\) increases (moving from left to right on the \(x\) - axis), the \(y\) - values of the function increase.

Answer:

Increasing on one interval and Decreasing on another.