Every Important Graph in Math

[@John-hw2ys]

I remember watching lengthy boring videos for hours just to know the conceptes that is explained here beautifully in a concise manner ... thanks a lot

[@Busybody007]

This is best video of graph on KZbin, very easy explanation

[@foxypiratecove37350]

For those wondering about why 0^(-x) is undefined for x ∈ ℝ+, it's because, keeping the condition x ∈ ℝ+, a^(-x) = 1/a^(x), and in the case of 0, this is 1/0^(x), and since 0^(x) is 0 (except for x = 0 that is left undefined by convention for some reasons), this is a division by 0 so this can't be defined.

[@isavenewspapers8890]

"why 0^(-x) for x ∈ ℝ+" I think you mean "why 0^(-x) *is undefined* for x ∈ ℝ+". Based on mathematical convention and on things you say later, I assume you're using ℝ+ to denote the set of nonnegative real numbers, which I'll keep in mind. You have to be careful about saying that a^(-x) = 1/a^x, because if a is 0, then for a negative value of x, you'll get a well-defined expression on the left and an undefined expression on the right. Maybe you're referencing the condition that x is a nonnegative real number, but that looked like it was part of a different statement. In this context, 0^0 is not an indeterminate form. An indeterminate form is a form that an expression in a limit expression can take, meaning that more work must be done to find the limit's value. This is not a limit. With that said, it is a common convention to leave 0^0 undefined, and it's also common to have it equal to 1. In either case, it's definitely not 0, so we can move on. Division by 0 actually *can* be defined. In fact, it is defined in certain systems, such as in the projectively extended real line. It's just that it's usually more convenient to leave division by zero undefined, so that's what we do.

[@foxypiratecove37350]

@@isavenewspapers8890 OH sorry I didn't noticed that I forgot to write a part. Thanks.

[@claudiocosta4535]

Another canonical form for linear graphs is X/Xo + Y/Yo =1 (similar to the equation of a ellipses but in first degree), where Xo and Yo are the intercepts on the X and Y axes, respectively (except the origin)

[@watch_2011]

At 7:22, You Swapped The Definitions Of Sine And Cosine.

[@Vasilis_Sky]

Amazing video! I especially liked that visualize everything, becauce in school we dont have time to deeply understand.

[@MikeB3542]

Dr. Gilbert Strang has referred to three: the polynomial; the trigonometric (sine, cosine); and the exponential, as The Great Functions. They are beautiful, their domains are continuous over all real numbers, and they are exquisitely connected to one another (Taylor Series, Fourier Series, Euler's Identity).

[@ocayaro]

You forgot Step, Impulse, Sigmoid

[@Bad11hokyky]

Thank you❤

[@walterbrownstone8017]

Lol this is great I'm going to just sleep with this video on repeat and then ace my math test!

[@simonstrandgaard5503]

Well explained.

[@MrConverse]

1:58, *and a is non-negative.

[@isavenewspapers8890]

This standard is not required by some authors.

[@MrConverse]

@@isavenewspapers8890 but then you don’t end up with an equation in standard form for each line, you end up with two.

[@ramashama-tw3ly]

🙏🙏👍👍

[@suryamgangwal8315]

In a straight line, shouldn't a,b, and c by rational numbers

[@foxypiratecove37350]

ax + b isn't linear in most cases. To be linear, it must cross the origin (b must be equal to 0). It's just affine in most cases.

[@ikonikgamerz3853]

Not necessarily, a linear graph just means that the function has to produce a straight diagonal line.

[@foxypiratecove37350]

@@ikonikgamerz3853 No. A linear function is a special case of affine functions. Affine functions are functions in the form ax + b. And a linear function is the case when b = 0, that means that the graph pass trough the origin.

[@masonv9333]

@@foxypiratecove37350 linear function (noun) 1. Any function whose graph is a straight line.

[@isavenewspapers8890]

Different authors use the term "linear function" in different ways. For a function f with real numbers as inputs and outputs, some authors use the term to mean a function whose graph is a line. However, other authors require that the function keeps the origin fixed; in other words, f(0) = 0 must hold. This term is relevant to the topic of linear algebra, which involves linear transformations, where the origin has to stay in place. In this alternate context, if a function composes a linear function with a translation, the term "affine function" may be used.

[@tinkeringtim7999]

​@isavenewspapers8890 in this case, the guy mixed up linear functions with linear _functionals_.

[@ikonikgamerz3853]

You forgot about the best functions of all: Constant functions (x=c) or (y=c)

[@isavenewspapers8890]

If we consider the graph of a function f as y = f(x), then x = c cannot be the graph of a function, because there are multiple y-values for a single x-value. y = c is just a special case of y = mx + b, where m = 0 and b = c.

[@ikonikgamerz3853]

@@isavenewspapers8890 vertical line rule ONLY works with f(x) = y X=constant is a function where f(y)=x

[@isavenewspapers8890]

@@ikonikgamerz3853 I will accept the idea that that's what you were going for, but you could've been clearer about it. Also, you can switch the x- and y-axes for any graph; why mention it only for this one in particular?

[@memeing_donkey]

18:04 😅

[@aravindmuthu95]

bro left out xy=1 form of hyperbola

[@ichigo_nyanko]

Is this your real voice? All the other before this sound like AI but this doesn't

[@imeprezime2591]

СВИ важнији графици из математике и физике су у књизи СРБИНА Руђера Бошковића. 12.08.2024.

[@saiaditya4787]

Nitaigaur

[@imeprezime2591]

И шта ту некоме није јасно? Вопроси есть? Вопросов нет. 31.08.2024.

[@hoeflikjedat]

I expected a dark mode video. Please Change your thumb to a white background.👍 Or better yet change video to dank mode. I'll watch them.all. but never ever in White blinding light 🕯️🚨 good luck

[@hillabwonS]

wowie

[@tinkeringtim7999]

Not bad, but clickbait titles.

[@gamesthatmatter9374]

eleven labs Ai voice used in this video lmao.

[@ThoughtThrill365]

nope, its a real human voice.