How to find the domain and the range of a rational function?

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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#math #algebra #mathbasics

[KambeFamily-ebvk]

this man is really CHAD solved all my probs and i have examm tmrww RESPECTT!!!

[generalkenobi]

respect to sir. have been doing domain and range for two grades and didn't understand as much as this 4 minute video explained. 😸

[Ninja]

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

[anonymouscheesepie]

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).

[johanndohmann]

nice t-shirt. good video, as usual. thanx a lot

[swatidwivedi]

😂😂😂😂😂wow what a wonderful amaging sir ....
From India 🎉❤

[PhumlileNyalunga]

I have a school assignment question can you help

[SomethingNiceBroo]

We're did u get that 3 did u divide 4 and 12?

[DogoBoy]

How would you know that this is a straight line, and not a parabola?

[SharonChola]

Good explanation but you are too fast😢

[bearecla]

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🫶

[likethiscommentifyouhatebt]

Can you please explain fermat's last theorem please

[censorthis]

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.