Question 1161128: Hi,
I had a recent math problem on an online math program that I ultimately got correct through brute force guessing, but I'm not entirely sure how it is supposed to work. It's difficult to describe in words, so I have included a link to what the problem looks like and my confusion with it. I am asked to describe the intervals that the function is decreasing, increasing, and constant at, but I am not sure how the answers match up with what the graphed function seems to indicate.
Image of graph and more detailed questions: https://i.imgur.com/JI03bW3.png
Thank you very much.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
When the program says "the function is increasing on the interval [2,3]", it means the function is going uphill when  . So if x is between 2 and 3, inclusive of both endpoints, then the function is going uphill. By "uphill", I mean you go upward as you read from left to right.
In contrast, the portion  is decreasing because the graph is going downill (as we read from left to right) for this interval. That's how they got the answer [-2,2]
The function is completely flat when x is between 3 and 5, so the interval would be  which is shortened to [3,5]
So in summary, we look at where the graph is going uphill, downhill or is flat. Then we record the x values to set up the proper intervals.
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