pre_calculus

Nama : Lucia Martika Yundarwiti
Nim : 07305144015
Prodi : Mat NR ‘07
Mata kuliah : BAHASA INGGRIS II
Hari/tanggal : Senin,01-12-08
Email : yoe_wiesheart@yahoo.com

VIDEO I
Pre_Calculus
Graph of a rational can have discontinuites has a polynomial the denominator.
For example
- The function of F(x) =
When x=1, so we change x=1
We get result = =
So (1, ) = not definited
When x=0,so we change x=0
We get result = = = -2
So (0,-2) = All right,
the solution of F(x) = ,is (0,-2)
- Missing point
To explain missing point,we give example of Y =
Missing point,happened when the nominator is zero and the denominator is zero
If we insert x=3
We get =
If we get ,and then we must make factor of Y =
With algebra :
Y = = x = x+2Þx = 3
The conclusion about missing point are :
Removable singulary :
- When x lead to ,and
- Factor and simply
VIDEO II
Limit by inspection
For Example :
If the higest power of x is greater in numerator

If the higest power of x is greater in denomerator.

VIDEO III
Examples:
1. The Figure Above Shows The Graph Of Y = g(x),if thefunction ,is defined by h(x) =g(2x) +2.What is the value of h(1)?
For,,,look for h(1),
We insert (1) to h (x) = g(2x) +2,and
We change x=1
So h(x) = g (2x) +2
H(1) =g(2.1) +2
=g(2) +2
=1+2
=3
The value of h(1) = 3
2. Let the function be defined by f(x)= x+1 if 2 f(p) = 20.What is the value of f(3p)?
What is f when x= 3p?
The f(x) = x+1
2 f(p) =20
F(p) = p+1 =10
P =9


And then we subsitusion p=9,in x=3p,so we get x=3p 3.9=27
x=27
for x(27) = 27+1
x=28
VIDEO IV
Rational function
Rational function of degree 2 :
In the case of one variable, x, a rational function is a function of the form
where P and Q are polynomial function in x and Q is not the zero polynomial. The domain of f is the set of all points x for which the denominator Q(x) is not zero.
An irrational function is a function that is not rational. That is: it cannot be expressed as a ratio of two polynomials.
If x is not variable, but rather an indeterminate, one talks about rational expressions instead of rational functions. The distinction between the two notions is important only in abstract algebra.
A rational equation is an equation in which two rational expressions are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected
Rational function of degree 3 :
The rational function is not defined at .
The rational function is defined for all real numbers, but not for all complex numbers, since if x were the square root of − 1 (i.e. the imaginary unit) or its negative, then formal evaluation would lead to division by zero: , which is undefined.
The limit of the rational function as x approaches infinity is .
A constant function such as f(x) = π is a rational function since constants are polynomials. Although f(x) is irrational for all x, note that what is rational is the function, not necessarily the values of the function.