Interval notation for where functions Increase, Decrease, Constant

Learn how to write Interval notation for where functions Increase, Decrease, and are constant in this free math video tutorial by Mario's Math Tutoring.

0:21 Example 1 Finding Where the Graph Increases, Decreases, Constant
0:53 Explanation of Why We Use Open Intervals
1:34 Hint on Using the X Values Not the Y Values
2:32 Example 2

Related Videos:

Interval Notation vs. Inequality Notation

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[vall]

I was unsure about whether to include brackets or parentheses when writing interval notion. I really appreciate your clarity on that. Just got a 100 on my math quiz! Thanks! :)

[goldenduper]

Thank you so much, I thought I would fail my math test but this explained the things i was confused about. I'm ready to go into my math test :) thank you so much.

[ghaniamessaoudene]

For me you are my favorite teacher, so great many thx for all infos

[Smiling_Tears]

With all due respect, I disagree that the answer to the question, "Intervals where a function increases" is (-infty, -2) union (1, infty) for one reason: that set is not an interval. An interval by definition has no gaps, punctures or holes. Because the question wants intervals, the correct answer is (-infty, -2), (1, infty). Those are intervals. Not every union of intervals is an interval, like your example. If the question was list the set of values where the function is increasing, then I agree with your answer: It is the collection of all values where the function is increasing, but to be clear, that collection is not an interval. In fact, if you had the union of two intervals that overlapped, that will be an interval! We can show that it is a necessary and sufficient condition. The only reason I'm posting this is because I tutor math and often the teacher's use weassign. I see students get this question wrong when they put union of intervals, and then the teachers don't have any justification for it, and I've seen them tell the students, "It's probably just a bug." But no, it's not a bug, and I'm tired of seeing teacher's claim that union of intervals, like your example, is an interval. This is as wrong to me as 1 + 1 = 5 using the addition operator on the set of real numbers. In short, your answer is a set, not an interval (although, just to cover my butt, an interval is a special kind of sets. So, all intervals are sets, but not all sets are intervals, and yours is an example). Cheers.

[DeezNuts-hhpw]

how come in the 2nd problem the first interval says increasing (-infinity, -3) instead of (-infinity, -2). Doesn't it stop increasing when x is at -2 or am I missing something?

[mathisbeautiful]

That constant interval you wrote should be in brackets. [-2, 1] You do need to include those points. To clarify, that constant interval on the graph can be written as the piecewise function: f(x) = { -1 if -2 less than or equal to x less than or equal to 1}. If you evaluate that function at -2 the output would be -1. Similarly if you plugged in -1.999 the output would be -1. You do need to include -2 and 1, there should be brackets.

[ironmanlifts]

Thanks for the videos. I plugged "U" as you mentioned and I got it wrong but I think that was my fault cause the answer should have been with ", " as mentioned in my homework instructions. The answer should have been (-oo, -4), (4, oo) NOT (-oo, -4)U(4, oo) .

[mohamedbarry]

Is it only when finding the domain and range where it includes the brackets?

[TheThrakatuluk]

Union notation should be avoided at all times. The word "and" will suffice. That is calc 101 and you failed