Answer:
(-∞, -1) U (0, ∞)
Step-by-step explanation:
To figure out which parts of the function are decreasing, we need to read the graph left to right.
Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.
How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.
The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).
Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).
Therefore, our final answer is (-∞, -1) U (0, ∞).