How to find the domain and the range of a rational function?
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- Опубліковано 16 жов 2024
- In this precalculus tutorial, we will find the domain and the range of the rational function f(x)=(x^2-2x-3)/(4x-12). This is a kind of tricky question because many students will just cancel out the common factor and make a mistake on the range of the function. Be careful!
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this man is really CHAD solved all my probs and i have examm tmrww RESPECTT!!!
respect to sir. have been doing domain and range for two grades and didn't understand as much as this 4 minute video explained. 😸
I remember in my classes where we need to find the range of rational functions with quadratic and/or linear terms, excpet most of them could not be “simplified”(i.e. you cant cancel stuff out).
The catch was them for most of them, we were not allowed to use pictures, and hence cannot use calculus(because most have max/min points which restrain the range). We had to use the discriminat of quadratic expressions to solve it algebraicly
in my midterm exam recently we had to find the minimum value of a rational quadratic function and at the time, I did not know about the cross multiplying discriminant trick, so I just pulled out calculus to find the answer lol
the formula of -b/2a save me tnx to the youtube video I have watched
@@leonardobuna5522 how would you apply that? bc im also struggling with range at the moment and I have no taken any calculus prior?
4x - 12 = 0
x = 3
f(x) = (x^2 - 2x - 3)/(4x - 12)
f’(x) = [(2x - 2)(4x - 12) - 4(x^2 - 2x - 3)] / (4x - 12)^2
0 = (4x^2 - 24x + 36)/(4x - 12)^2
0 = x^2 - 6x + 9
x = 3 is where the extremum would normally be, but f(x) has an asymptote at x = 3
so we test 4 values in f(x): - inf, + inf, 3- and 3+
f(- inf) = - inf
f(inf) = inf
f(3-) = - inf
f(3+) = + inf
The range of f is (-inf,3)U(3,inf).
nice t-shirt. good video, as usual. thanx a lot
😂😂😂😂😂wow what a wonderful session..... amaging sir ....
From India 🎉❤
awesome, thanks!!
how did you do the thing ontop
I have a school assignment question can you help
You teach very good
I had this yesterday
Good video
We're did u get that 3 did u divide 4 and 12?
4x=12
x=12/4
x=3
How would you know that this is a straight line, and not a parabola?
when you simplify the highest power of x is 1 so it has to be a straight line
y=mx+c
the simplified function has degree one, hence the st line
X has power of 1 so its a straight line. Try plotting y=2x+1 or y=x+2 on a graph. You will get a straight line. You will get parabola only when the function looks like y=x²+2 or y=x².
Good explanation but you are too fast😢
Slow down the video speed
Pickup the pace noob
I think you are too slow 🐢🐢🐢🐢🐢🐢🐢🐢🐢🐢🐢🐢🐢
Skill issue 🐢
Ignore these degrading replies Sharon, keep practicing in math and maybe in the future you'll be able to pick up the pace! ❤
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As a dumbo in math and had watched so many vids about this certain topic, you explained it better than my math teacher HAHAHAHHAHA. Thank you so much. You explained it better in 4 minutes than anyone else🫶
It's incredible to me how many people on youtube don't understand or bother understanding that a lapel microphone is meant to be clipped on a shirt. Its literally why it has a clip. The sheep see one youtuber holding it , and the rest just mimic the same. monkey see, monkey do.
Bro calm down, your really getting pressed over a microphone, this isn't even a mic review, this is a math teaching bro, golly bro your prolly like 10 years old