Graphing Algebraic Functions: Domain and Range, Maxima and Minima

[@superstitiousdead]

I almost failed Algebra 2 last year, and now I’ve pretty much recuperated all of the knowledge I’ve lost through this series and a little Khan Academy. I hated doing math a week ago. Not anymore! The brevity and clarity of these lessons are a blessing. Thanks, Dave.

[@adityadhardwivedi634]

I think that it would be a starting for the lessons of Calculus thanks for that professor Dave

[@adityadhardwivedi634]

@Adam Dangelo You're next level mischief maker.

[@bindusnathan318]

I am very thankful to you proffesor dave

[@roblovestar9159]

Hey professor! I think you tricked us when you relabeled relative maximums and minimums to local maximums and minimums... ;)

[@raheennock9502]

Great video 💯

[@ignacioleikis1784]

Spoilers! Does local maximum = relative maximum and local minimum = relative minimum?

[@MichaelLeightonsKarlyPilkboys]

Yep, local and relative are interchangeable.

[@aveinmovil]

im wondering what happend if you rewrite a given function as "(a) times 1" where "a" is the function and you express that "1" as a "x-b/x-b" where b is a real number. That will create a void spot in the domain out of thin air! Can you please point out the mistake in my reasoning?

[@rosepierce9382]

Aren't you essentially multiplying two functions here? x-b/x-b could be defined as another function and multiplying two functions can change the set of domain values, as far as I understand.

[@aveinmovil]

Thank you for answer! but that function is equal to 1 so it does not change the function that is multiply by it.

[@rosepierce9382]

@@aveinmovil Yes, but the domain of this new function x-b/x-b is all real number values except 'b'. So the domain has changed. Now, when you multiply them together, you get a new domain.

[@tGoldenPhoenix]

Done this lesson.

[@calebabudu831]

Do you give notes?

[@فرامرزلشنی]

a vertical line cant be a function(unless you exchange x and fx axis). was it an intentional mistake? thanks.

[@NickHope]

Yes. 03:14. It's a strange one and I'm still trying to figure out what he meant. Even if he meant f(x) = 3 then the domain is still all real numbers and it would be the RANGE that is limited to just 3.

[@younezzz]

داداش بیا یکم به مام ریاضی یاد بده اگه هستی 😂

[@rosepierce9382]

I'm sorry, but can someone tell me why vertical lines can't be defined as functions?

[@Red_Angel-dw4cv]

​@@rosepierce9382it would fail the vertical line test - a test to tell if a graph is a function

[@athulsebastian3792]

Graçias Señor

[@vaibhavgiri2820]

u r great

[@mustafasaber5076]

Relative maximum Relative minimum Even, odd

[@hellogoodguy64566]

slow down a little