SENTENCES

STIPULATION= Ketentuan, syarat; Certainty (rule, direction) that must we do
example :if we want to enter a college, several STIPULATION is waiting us.

ELABORATED= Merinci atau menekuni; an activity(learn,etc) with diligent
example :the student of mathematics should ELABORATED math.


JURING= Section, Segment of the cyrcle
example :in a circle, we can make a SEGMENT, with just one line.

BERSISIAN= Adjacent; from side to side.
example: we can make several adjacent in two form.

Representing video of learning mathematics (video 3)

Pre-Calculus
• Graps of a rational function
Can have discontinuities
Has a polynomial in the denominator
It’s possible that some value of x we’ll need to division by zero, if so that value is straight up OFF LIMITS
Example: f(x)=(x+2)/(x-1), and take x=1, then we get f(x)=3/0, with zero in the denominator(that’s no good), so choosing x=1 is a bad idea(baaad).
3/0 is break in Function Graph
Not all rational functions will give zero in denominator, for example is f(x)=1/(x2 )+1, the denominator is never zero because of the +1, so the graph is no break, and don’t forget as general rule, when you deal with Rational function, you must expect the possibilities that the denominator is can be zero.
Break can show up in 2 ways:
1. Missing point on the graph,
Example: y=(x2 –x-3)/(x-3), when we take x-3 the result is 0/0, this is Tyical Example of Missing Point Syndrome.
Missing point is a kind of a loophole,
y=(x2 –x-3)/(x-3), when we take x-3 the result is 0/0, but if we simplify first, we got
y=(x2 –x-3)/(x-3)>>>y=(x-3)(x+2)/(x-3)>>>y=x+2.

TASK OF ENGLISH

STIPULATION= Ketentuan, syarat; Certainty (rule, direction) that must we do
example :if we want to enter a college, several STIPULATION is waiting us.

ELABORATED= Merinci atau menekuni; an activity(learn,etc) with diligent
example :the student of mathematics should ELABORATED math.


JURING= Section, Segment of the cyrcle
example :in a circle, we can make a SEGMENT, with just one line.

BERSISIAN= Adjacent; from side to side.
example: we can make several adjacent in two form.

From: Bibid Bagasworo
NIM: 07305141013
class: Math R '07
Yogyakarta Math University

Representing video of learning mathematics(video 2)

We will describe the video that I’ve been looked, the video content some question, these are:
13.the figure shows the graph of y= g(x). if the function h is defined by h(x) = g(2x)+2, what is the value of h(1)?
First piece of information is h(1) then y=g(x) and h(x) = g(2x)+2 then we count h(1)=g(2)+2, refer to the graph g(2)=1 so h(1)=1+2=3 is the answer.



In another question:
13. Let the function f be defined by f(x)=x+1. If 2f(p)=20, what is the value of f(3p)?
Answer: first information is f(x)=x+1
second information is 2f(p)=20
2f(p)=20f(p)=10, because f(p)=p+1=10, so p equals to 9, we looking for x, so x=3px=27,is this the answer? No, we looking for f(3p)f(27)=27+1=28 is the answer

Representing video of learning mathematics (video 1)

F(x,y)=0,
Function=f(x) : VLT
Function x=g(y) : HLT :INVERTIBLE



===>y=2x-1 and y=x ;
We can find the intersection by ===>
x=2x-1 ;
1+x=2x ;
1=x ;
so the intersect is 1
2x-1=y
2x=y+1
x=(1/2)(y+1)
x=(1/2)y+(1/2, excange x become y, we get
y=(1/2)x+(1/2)
example;


f(x)=2x+1
g(x)=(1/2)x+(1/2)
f(g(x))=2[(1/2)x+(1/2)]-1
=x+1-1=x, In the other form we have g(f(x))=(1/2)[2x+1]+( 1/2)===>
x-(1/2)+(1/2)=x
g=f-1
f(g(x))=f(f-1)
=x
g(f(x))= f-1(f(x))=x
let’s do one more example, we take y=(x-1)/(x+2),in vertical asymtot in x=-2, and horizontal asymtot in y= 1, the x intercep is going to (1,0), the y intercept is (0,1/2)
we make the equation simple to be calculate:
y(x+2)=x-1
yx+2x=-1-2y
(y-1)x=-1-2y
X=(-1-2y)/(y-1)
Y=(-1-2x)/(x-1)
When x=0 ,y=-1, then when y=0,x=-1/2, so we get graphic that have vertical asymtot x=1,and the horizontal asymtot y=-2,
So f-1 (x)=(-1-2x)/(x-1)
f(f-1 (x))= ([-1-2x/x-1]-1)/([-1-2x/x-1]+2)
=[-1-2x-(x-1)/(x-1)][(x-1)/(-1-2x+2x-2)]
=(-1-2x-x-1)/( -1-2x+2x-2)
=-3x/-3
=x
Back to the front statement, is
f-1 (x)= (-1-2x)/(x-1) and
f(x)=(x-1)/(x+2), so
f-1 (f(x))= (-1-2{(x-1)/(x+2)})/({ (x-1)/(x+2)})-1
=-x-2-2x+2/x-1-x-2
=-3x/-3
=x
F(g(x))=x,wich the range of g is domain of f
G(f(x))=x,wich is the range of f is domain of g
G= f-1 it’s important thought, to remember, the (-1) it’s mean the reciprocal or it’s just mean invers function, when we doubt line we found out the slope of the invers function with the reciprocal of the other slope,that’s true general.