•´¯`•» zeroeѕ oғ a ғυncтιon «•´¯`•

Oh, welcome back to Mathland, dear guests.

I hope you have not missed it too much!~

Today, we will be journeying to the White Queen's domain for a quick visit. On our way their, we will be discussing the zeros of a function.

Please do not get lost now.

Let us begin.~

Through the uses of synthetic and long division, we are able to derive the zeros of a function. First, you would plug the zero into the function given and if there is no remainder, than it means that the equation does indeed work. 

To find the zero of a factor - for example (x-3) - one must first set the equation equal to a zero and then either subtract or add determining on the sign it was previously.To clarify any confusion....

and

This indicates that once you plug in a zero to the function, the answer that come out will be the zero of the function.

However, when using long and and synthetic division, if a remainder appears once it is divided, then it indicates that the equation does not work. 

The significance of the zeros is that they are incorporated into almost every aspect of math.

Hmm...I believe that is enough for today.~

Well, it seems that we have arrived at her Highness's court.~

Oh my, it seems that the Queen is up to her mischievous cooking once again.

Good bye for now.~

º× pιece wιѕe ғυncтιonѕ ׺

Well well well... what a fancy place to meet.~

It's been quite some time, dear guests. Have you missed the lovely Mathland?

Would you like to get started?~ 

After all, this tea party is beginning to feel a bit dreary...

Shall we be on our way then?

Today, I will be taking you personally to the Queen's castle - but please be careful. She erupts into a rather large fit when things do not go her way. Please do not anger her or you just might possibly lose you head... 

Ah, it seems that we have arrived! I welcome you, dear guest, to the treacherous Heart Kingdom...

Today, we will be touring the palace and learning about the notorious "Piece Wise Functions". These functions will either be continuous or discontinuous when graphed. Meaning, when one places their figure on the line, if the finger must be lifted to transition, then it is discontinuous - and vice versa.  During the solving of these equations, there may be absolute value signs around the equations, to deal with these, you simply treat them as if they weren't there. After that, simply solve them regularly and out will come the answer. Next to the equations will be limits that tell you how far you may go: x less 0, equal to 0, greater than 0, etc. By using these limits, they specifically detail the placing of the graph. In addition -

"OFF WITH HER HEAD!!!!"

Oh my, forgive the interruption...it seems that the Red Queen is at it again. Well, this does certainly also help elaborate a point. The limits of the functions can be paralleled to how all the roses in the Queen's must be Red or else they will cease to exist because the Queen will behead those who did not paint them Red. This is partially why all the card soldiers are so diligent in making sure each and everyone is painted.~

I believe that is enough for today, since I seem to have to go pacify the Queen's tantrum currently. I do hope you enjoyed today. Please do visit again soon.~

Farewell lovelies!~

Have a wonderful rest of the night...

• ѕυperнero тranѕғorмaтιonѕ •

Welcome back lovely guests of wonderland.~

Today, we have a special event prepared by the Queen of Mathland!
We will be journeying with our new friends, the F(x) men! Allow me to introduce each of them:

And,

These superheroes are in charge of keeping Cartesanville safe from evildoers! By eliminating these baddies with their powers, they each demonstrate their own specific technique that is unique to them. Lady Straightedge has the function of f(x)= x, while Pawabawas the equation of f(x) = x^2. Robo-grow is f(x) =2^x, and Captain Abs is f(x) = |x|. Last but not least, Radical girl is f(x) = √x, and Bipolar Tommy is f(x) = x^2.  Below are some of their great accomplishments!~

All these superheros sure do remind me of how our dear Alice defeated the Jabberwocky and saved Mathland.~

Well, I must retire for now, I do hope you enjoyed this event prepared by our lovely Queen.

Farewell.~