Understand Domain and Range

Understand the domain and range of a function. The domain is the set of all values that can be input into a function and the respective output values are the range. There are restriction to the domain in terms of the real number system which the video will explain.

[pestbear]

I wanted to first give God the praise for allowing me to find you on youtube. I am 44 yrs old and have not been in school in over 20 yrs. I was having trouble trying to get my high school diploma at the beginning of the year and could NOT pass geometry. I decided to go for my GED instead at the end of last month. Math was my biggest obstacle until I found your channel. You take the time to breakdown every step of the equations no matter what lesson it was. I took my math GED test today and passed after studying and practicing with your videos and website for the last 10 days. THANK YOU, THANK YOU, THANK YOU.

[bobdane]

Who came here because theres a test tommorow and your teacher doesnt know how to teach

[nickdegange]

Set playback speed to 1.25. You can thank me later

[SS-ygyo]

Excellent explanation. Thank you for it. Million times clearer than my son's math textbook!

[leafpelt]

I was scrolling around when I found this video, which seemed to be about the part of math I needed to study for. It was and even as a not native English speaker I understood it and it helped me greatly, thanks!

[aminakhan]

why cant youtube teachers come and teach at schools 😭 scl teachers are shiiiitttt .
this video is soo goood ughh.

[Ro-tntp]

This is the best explanation of functions I have come across yet.

Coming from a machining/tool-making background, now studying computer science, I have just seen at around 7 minutes in, why I should be learning functions.

This is good teaching. The light bulb moment for me! I learn in pictures and visuals as well as a physical mechanical understanding.

The way some teach these things, it's like trying to follow someone speaking some alien talk!

[ginadeleon]

Very easy to follow. I like how its simplified. I don’t speak math so this language lesson helped me to understand. Stick with the lay terms concept. It worked great for me. Thank you. The whole machine and breaking it just really helped Thank

[Francis-fori]

First 4 minutes and I finally understood it. You made it too easy to understand. Thank you.

[rocioaviles]

Thanks to you I passed my math GED!!! All i did is followed your lessons on you website! Thank you so Great teacher!!

[victoroluwabiyi]

Thank you very much. I've been trying to understand this for sometime now but once I watched this video, all question were answered.

[GoldenKeeper]

My true humility to your explanations that are broken down and gentle to be able to comprehend. I am in the midst of learning this topic over the weekend to finish it fully. Thank you❤️❤️

[thevminist]

Came here because I don't understand my teacher. :/

[stalex]

I paused this video to say Thank you!
You are the first one, who mentioned imaginary numbers while talking about square roots of negative numbers. Everybody else just say "there is no sqr roots of negative numbers" and go on...
Again thank you

[nicolewisse]

i procrastinated learning this and now it’s the summer before 9th grade and i feel the need to finally learn this because i’m stressed that imma need this

[amyb.]

Thank you. This is the most helpful, basic video on this subject I have found.

[marilynmiller]

** VIEWER BE WARNED: Overall, useful video. There are some errors that need correction. First, for y= sqrt(x). Mathematical notation has the rule (i.e. writing convention used in mathematics) that the radicand itself represents the POSITIVE square root of your domain element; NOT both roots. If you mean both roots, your equation would have the "plus or minus" symbols preceding the radicand, (and as described in a later sentence, would violate the definition of function altogether.) Therefore, the range of y = sqrt (x) is the set of all numbers greater than or equal to zero. A graph of the basic function corresponding to your equation will confirm this. Another thing to note is that IF you mean the radical function with index 2 that actually WOULD include both roots, the graph of that shows that the graph fails the Vertical Line Test AND the relation format shows that this gives you TWO distinct ordered pairs with the same first element. So, including BOTH roots in what was written says that the example used would not even satisfy the definition TO BE a function. Yes, there is still a "domain" in the sense of input; however, it is not the domain of a FUNCTION. Second, for x squared +2; the range is NOT all real numbers; rather, it is the set of all real numbers greater than or equal to 2. The function is that of a parabola with vertex at the point (0, 2) i.e. the "basic" or "parent" quadratic function with a vertical shift up 2 units. (Review linear transformations of functions.) y=2 is the minimum y value because this parabola opens up. Again, this can be verified with the graphing calculator. These facts that I have stated can also be shown in any textbook covering Algebra I (Math I ), as that course covers both of these relatively simple functions. I had planned to send the link for this video to my College Precalc students for review purposes. Luckily, I previewed the entire video before doing so. And those of you who come here because your "teacher doesn't know how to teach" need to be aware that videos such as these are quite useful; sometimes your teacher DOES know what s/he is talking about. Take ownership of your learning so that you don't need to rely solely on an instructor. And remember that not everything you find online is necessarily accurate. You should use videos such as these as reviews, and understand that if anything disagrees with what your instructor and textbook say, you need to do additional research and verify what is actually correct. (And, yes, I am absolutely correct on what I have pointed out, so I will not be engaging in any argument on this.) I do hope the author of this video will make corrections (just as Sal Khan has had to do for some of HIS videos), and post a comment on my comment that corrections have been made.

[angelia]

"If you're watching this video, you're probably in Algebra 1"
Me taking Algebra 2: 👁️👄👁️

[norsauve]

Thank you for explaining it in a simple way. The virus has made school hard especially the fact that I’m a 7th grader taking high school algebra. Thank you!

[dsalinaspk]

Thank you, Thank you, Thank you. Fantastic way to make a old man like me understand.