Calculus Midoriさんのイラストまとめ

>The graph will intersect the x-axis at those points. How the line interacts with them, whether it "bounces" or "crosses", is determined by the multiplicity.
>Multiplicity is just a fancy way of saying "how many times 'it' appears."

>It only takes one zero, one traumatic experience, to turn the purest of hearts in beautifully blackened ones. It's a metaphor though!
>If numbers could really do that instead of turning the y-value into 0, I'd be concerned...
>(He's forgetting about someone...)

>x=-3, 2, -1... Those are the zeros.
>When you plug in either of those, one of the factors, (x+3)(x-2)(x+1), will be canceled into a 0. It's a given, but 0 times anything is zero.
>For example, if we plugged in x=-3...
y=((-3)+3)((-3)-2)((-3)+1)
y=(0)(-5)(-2)=0

>Surprised? My innate floormaster spirit kicked in, you better forgive him or he won't forgive you! Haha.
>Yes though, it can intersect the x-axis any less than 6 but no more than 6 as well. The possibilities are finite.
>Here in the example, there will be only 3 zeros.

>First we'll put on our thinking caps for the end behavior.
>In its expanded form, the highest exponent of the leading coefficient will be 6.
>That means the graph can cross the x-axis to a maximum of 6 times. But it can also intersect 3...2....1.... GAME OVER.

>We won't cover horizontal and vertical asymptotes for this example. You only need to worry about them when a denominator is present.
>And plus, I wouldn't want to overload your brain. People are more interesting when they're functional! There's no fun in breaking a broken toy.

>Continuing on, it's in factored form. Factored form is significantly more helpful since it gives us the zeros on sight.
>A "zero" is the x-value that when plugged into the function, will yield a y-value of zero. Graphically, they're intersections through the x-axis.

>Usually they'd never be as pretty or as simple as this, but we all need to start somewhere.
>I'm using the example from https://t.co/WxVAIQwNLV , so refer to that more a in depth explanation. I would create a polynomial myself, but ehh. Nah. Nope!

>So.. I said I was going to cover graphical transformations... But I've decided against it.
>I'll be covering how to sketch functions without a calculator today, since I'm way too disinterested to spend another day on concepts alone.
>We'll be using this polynomial as an example:

>I say that because you know... I died and all, murdered and left on the cold pavement! It was cruel of Alice to leave me like that. I'm still upset to this day.
>Even I'm capable of expressing such hate. A smile that holds a thousands words and feelings! That is me, Sou Hiyori.