isn't it supposed to be, for the range, a positive 2? If you do the same idea to the denominator once you are looking for range, it would be x = 2. If not, why would x -2 still be x = -2 for the range? :"""{
Thank You So much! Our teachers at school just solve the questions and expect us to understand and when we ask questions, they make fun of us. So this was really helpful, thank you
After 10 years I through myself into a algebra 2 class and I feel like quitting. Too late to drop the class. This is the only channel keeping me alive in this class 👏🏻👏🏻👏🏻when I’m lost I come here 💯
I really wish I had you as a teacher many years ago Brian, I'm at university and the tutor/lectures may as well be speaking a different language, you make math make sense.
Fastest way of finding the range: Since the degree of both numerator and denominator is the same, just divide the leading coefficient of the numerator which is 2 by the leading coefficient of the denominator which is 1 that will result to 2. Therefore range=(-○○,2)u(2,○○).
@Harris Park really? please enlighten me about this, cause I've tried lots of rational functions and they seem to be working well... Not sure about rational functions with holes tho
Thank you! This is the best example I've seen and I have spent days trying to figure this out. It's like, everyone else seems to be able to skip the 'math' of it in broken down steps. Also, no one else has shown how to flip the variable and solve for the inverse function to find the range. The crazy part is, this is like chapter 1 in a lot of algebra books! And I can do the rest of the book just fine but domain and range of algebraic functions has always been my achilles heel. Hopefully, not anymore. And I know it's important because I want to get into some calculus soon and that whole subject seems like it's basically full of functions. Thank you again. You're my favorite math tutor on youtube because of your process and just the way you communicate idea. A lot of math teachers aren't always the best with words.
I am so thankful to have found this video, many of my previous teachers would take much longer to explain this process and I really appreciate your help. You are very good at explaining things in a sensical way!
Thank you so much, you're the first video that makes sense ,other tutorials avoid doing fractions and do easy equations instead which I find pointless but you explained this very well
Thank you so much I wasn't able to determin the range on a fraction equation. But now im better thank you... I hope youre still doing these videos im going to subscribe now on the channel ❤
Why did you do all this Sir ! It was simple at first ! THAT'S MY SOLU y=(2x-1)/(x+4) xy+4y=2x-1 xy-2x=-4y-1 x(y-2)=-4y-1 x=-4y-1/y-2 SO Range is all R exepting 2 Tell me plz if it's true
I never understood why we used the x in the inverse function to predict the range But my math teacher will always be like ....domain : possible x values .....range : possible y values So can't we just make x the subject in original eqn and 🤔 about possible y's.....and leave swapping of x and y to inverse alone?
the best and fastest way to find the range is to use the concept of horizontal asymptote. Let the degree of numerator = P and the degree of the denominator = Q then a) if P>Q, then there's no horizontal asymptote. b) if P=Q, then divide their coefficients c) if P
So...if it does not work everytime, then you probably shouldn't post this comment. Here is the problem: What if someone doesn't know about the "holes"?😢
Isn't the first step by finding the domain you set it not equal to zero. You set it to just zero but the denominator cannot equal zero so you have to set it not equal to zero. Like an equal sign but with a line through it. So shouldn't the domain be [-4,all real #).
سبحان الله وبحمده سبحان الله العظيم 🌼🌷🌼🌷🌼🌷🌼🌷🌼🌷🌼🌷🌼 اللهم اني اسألك الهدى، والتقى، والعفاف، والغنى، والمغفرة من كل ذنب. 🦋🌹🦋🌹🦋🌹🦋🌹🦋🌹🦋🌹🦋 اللهم اني اسألك النجاح والتوفيق ⚘
hmm, well that is more advanced than what I teach so when you swap variables look for algebraic techniques such as completing the square or dividing that can help you isolate the y. There might be an easier way but I am not sure of the right methods without spending time looking it up as I do not recall
Please does this method of calculating the range work for all rational functions? How do I find the range of (3x-8)/x squared-9x+20? Thanks for the video
I never understood why we used the x in the inverse function to predict the range But my math teacher will always be like ....domain : possible x values .....range : possible y values So can't we just make x the subject in original eqn and 🤔 about possible y's.....and leave swapping of x and y to inverse alone since that works too?
Hello Sir, What about this question? I have been trying for a few hours and i can't seem to get anywhere close. I managed to find the domain which is (2
