Question

find the open interval(s) where the following function is increasing, decreasing, or constant. express your answer in interval notation.

Explanation:

Step1: Analyze the function's slope

A function is increasing when its slope is positive (going up from left to right) and decreasing when its slope is negative (going down from left to right).

Step2: Identify intervals

Looking at the graph:

• For the decreasing part: From the left - hand side of the vertex (where the function changes direction) to the vertex. The vertex \(x\) - coordinate is \(3\). So the decreasing interval is \((-\infty,3)\).
• For the increasing part: From the vertex to the right - hand side. So the increasing interval is \((3,\infty)\).

Answer:

The function is decreasing on \((-\infty,3)\) and increasing on \((3,\infty)\)