At beginning of class on friday we first went over long - non caculator and caculator allowed tests. Although, chapter 7 was one of hard and boring chapter, we were able to survie and got a decent average class test score! Mr. Cope compliment us that he never had strong Advance Algebra class like this! Yeay, good for us. I hope everyone will keep up good grade in Advance Algebra! After we went over our test, he introduced chapter 8! I was little scared (?) to learn complicated math after chapter 7 , because I felt little chellenged after chapter seven. (I'm pretty sure everyone felt that too).
Then Mr.Cope passed out the 8.1 note-sheet. Soon as we saw the worksheet,we noticed
something familiar , a funtion f(x) that we learn in chapter 1! When you have funtion f(x), we learn that we have to plug in a value for X in a equation.
Well, If we know one thing we know another thing!
If we know how to solve f(x), we should also know how to solve f(g(x)).
But! Before we try to plug g(x) in to "f" funtion. We first need to solve funtion g(x) and plug that number in to"f" funtion. It is the same idea as chapter one, but we have 1 extra step. Because its funtion in a funtion. And this is called "Composition of Funtion".
If you are still confused, think about the Babushka Doll (From, Russia) that many of us played when we were young! How to play is simple, little doll goes in to bigger doll and bigger doll goes in to next bigger doll. So I hope you get the Idea!
Now, lets do some math!
Let p(x)=x+5 and s(x)=x^2 Find s(p(7)) and p(s(7))
To solve funtion S, we need to first solve a funtion p(7).
Plug in 7 in to equation p(x)=x+5 which result in p(7)=7+5=12!
But, 12 is not our final answer.After you find a answer to funtion inside of a funtion,plug that number in to the outer funtion.
Plug in 12 in to equation s(x)=x^2 which results in s(12)=12^2=144.
If you want to solve funtion "P", find the funtion "S" first and plug that answer in to funtion "P".
Its exactly the same way as solving the funtion "S".
Last thing that we learn end of the class was how to read composition funtion when
written like this : s o p(7)
s o p(7) is also same thing as s(p(7)).
For exmaple, if you want to write y(x(8)),first take Y(Outer funtion), put "o" in a middle. Then write x(8), which looks more simplier than y(x(8)).
So y(x(8)) will be written like this : y o p(8).
Even if they do not give this written on a problem > y o p(8) OR y(x(8))
You can still solve a problem by finding by yourself.
I hope this review was helpful to everyone.I am not the funnist writer in the world, but
I can teach you math! I hope you enjoyed it, good luck rest of semester!