Given rational function find the vertical asymptote and hole
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- Опубликовано: 13 окт 2024
- 👉 Learn how to find the removable and non-removable discontinuity of a function. A function is said to be discontinuous at a point when there is a gap in the graph of the function at that point. A discontinuity is said to be removable when there is a factor in the numerator which can cancel out the discontinuous factor and is said to be non-removable when there is no factor in the numerator which can cancel out the discontinuous factor.
To find the discontinuities of a rational function, it is usually useful to factor the expressions in the function and we then set the denominator equal to 0 and solve for x. The value of x for which the factor appears in both the numerator and the denominator is the point of removable discontinuity while the value of x for which the factor appears in only the denominator is the point of non-removable discontinuity.
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this man is my teacher right here. I hope you make a math tutorial for SAT And ACT in the future topic.
will plan to do that kind of stuff in the future
@@brianmclogan YESSS
This dude is my teacher, the one in school can’t explain as well or teach as well
My teacher has a deep accent and makes a decent amount of mistakes in his English so it's also hard for me to learn from him. He seems like a really nice guy though.
On everything
Bruh my genmath teacher is teaching us wrong ideas and stuff and one time I told him respectfully that what he taught about the horizontal asymptotes is wrong, he insisted that he is correct and I tried to show him my references and ask him why is he correct and then he ignored my messages (online class). And now hes acting rude towards me during classes
Same mines goes too fast and doesn’t let us practice much
especially your English teachers
Omg you’re a life saver. My algebra teacher has more screws loose than a faulty ladder. And she is about just as emotionally stable. This video really helped me get the hang of this! Thank you
My teacher told us she won’t be writing out problems on the board at all...it’s only the second week of school and this guy is my savior
This guy teaches me more than my actual math teacher
My math teacher explained this 50x more complicated. I didn’t get any of this until now.
a hole is the opposite-sign-version of whatever you cancel out in trying to find the VA
If you have y = P(x)/Q(x) where P(x) and Q(x) are polynomials, then you should factor P(x) and Q(x). If P(x) and Q(x) have any common factors, then those common factors give you the holes. Any factors of Q(x) that are _not_ factors of P(x) give you the vertical asymptotes.
Let us see that in action: in this video, we have P(x) = (x - 4)·(x + 3) and Q(x) = x + 3. Notice how x + 3 is a factor of both P(x) and Q(x). Hence, x + 3 gives us a hole at -3. Does Q(x) have any other factors? No. Thus, there are no other holes, and there are also vertical asymptotes.
With online learning this mans is literally the only thing making sure I actually understand fundamental things in class.
Crystal clear presentation. Thank you.
If I had just watched this video earlier, I would have saved myself an hour of frustration. Thank you.
The most concise explanation of this concept I've found yet. Thank you so much.
happy to be able to help!
bro ive been confused all day and u just helped me in less than 5 minutes THANK YOUUUU
I got a test in two hours you're saving me with this video 🙏
Thank you for posting. My teacher didn't explain this as well. wow, now this actually makes sense. Haha
I ace all my tests cuz of u, thank you!!
still dont know what the hole is. i know what it is on the graph but how am i finding it? is it the intercepts or the points or what? i hear holes twice and thats it
same i've been trying to find what a hole is and no videos say what it is.
the holes are just the values that cancel out from the numerator or denominator and to find the y-value you plug in the x-value into the equation
Eshaan Tandon oh you saved me, thank you SO much!!
When u factor, what ur cancelling to simplify is what ur hole is going to be
If you have y = P(x)/Q(x), then the first thing you should do is factor P(x) and Q(x). Their common factors give you the holes. Whatever factors of Q(x) are _not_ common with P(x), those are the ones that give you the vertical asymptotes.
He is our mathematical savior and thus I give him the nickname Math Overlord Mclogan
U said up until this class period that the asymptote being -3 is ok. Does that mean in this case that there is no asymptote? Or that that it is still at -3.
This man is goated during this time of online school
perfect short and sweet explanation that is easily understood. thanks!
Explained so clearly 👍🏾
Thanks!
Is hole the same thing as a pole? My math book says "poles and asymptotes"?
Ohh,it makes so much more sense now. Thanks for the video! :)
So do u find the asymptotes before or after u simplify??
After
Can't we write the domain and range in these forms : Domain = (-inf,-3) U (-3, inf) ... Range = ( -inf,-7) U ( -7, inf )
absolutely
saving my life in grd 11 functions rn
This helped me out so much!!!!
i was so tired in class today so here I am trying to catch up🤣🤣
I left a comment
THANK YOU SO MUCHH
I still don’t understand what the hole is in this equation. Can someone tell me what the hole is?
-3 is the hole, because x + 3 = x - (-3) is the common factor shared between the numerator and denominator.
omg so damn good！ thank you very much
What happens if I get a hold of (2, 8/0)
You will get (2,0)
I know I’m late but 8/0 would be invalid. It would be only a 0 once it is a 0/8.
fuck i wish u were my teacher fr pre calc