STRETCH Optional 1 Describe how you can tell from an equation whether a function increases, decreases, or is constant.

To determine whether a function increases, decreases, or remains constant from its equation, you can analyze the function's derivative. If the derivative is positive over an interval, the function is increasing there; if it’s negative, the function is decreasing. If the derivative equals zero, the function is constant in that interval. For polynomial functions specifically, looking at the leading coefficient can also give hints about the end behavior, helping to gauge changes in the function's value. Additionally, you can use the concept of critical points obtained from the derivative's zeros. By testing intervals around these critical points, you can identify where the function changes behavior. Plotting the function or using a sign chart can also visually confirm where the function is increasing or decreasing. These techniques provide clarity and assist in sketching the function accurately!