Question

1. determine the interval(s) on which the function is decreasing

enter your answers using interval notation
remember, if it is increasing or decreasing on more than one interval, you must use the union symbol between the two intervals

Explanation:

Step1: Identify decreasing interval

A function decreases when its graph falls as x increases. From the graph, the function rises to a peak at x=0, then falls until x=5, then rises again. So the decreasing interval is between x=0 and x=5.

Step2: Write in interval notation

Use open parentheses for interval notation (since the endpoints are where the function stops decreasing/starts increasing, we use open intervals for continuous decreasing behavior here).
$(-\infty, 0)$ is increasing, $(0, 5)$ is decreasing, $(5, \infty)$ is increasing.

Answer:

$(0, 5)$