Nama : Dina Nerisa

NIM : 07305144003

Prodi : Matematika Non Reguler 2007

No. HP: 085292974835

Email : dheena_cut3@yahoo.co.id

Bahasa inggris II / selasa jam ke III

Video I

Precalculus is graphs of a rational function.

It can have discontinuities has a polynomial in the denominator, where denominator have value is 0, so the value is infinite.

We can see one example in below :

If we insert , the numerator value is 8, and denominator value is 0.

So, if 8 divided by 0 equals infinite. is bad choice and discontinuities function graphs.

If we insert , the numerator value is 6 and the denominator value is -2.

So, if 6 divided by -2 equals -3. and break in function graph.

But, not only all rational functions will give zero in denominator. This matter depend to kind of equation.

Rational function denominator can be zero.

Polynomial

zero in the denominator.

Smooth unbroken curve.

Example :

If we insert , we find become

This equation give value is infinite. It is not possible, not feasible, and not allowed. The other ways to determine value from this equation is use factoring numerator ang divided by denominator.

Then we insert in , so the value of = -9.

Missing point is a loophole.

Example :

If we insert ,

Video II

Limits by inspection have two condition. This condition is

1. goes to positive or negative infinite.

2. Limit involves a polynomial.

Polynomial over polynomial

Example :

The key to determining limits inspection is in looking at the power of . If the highest power of is greater in numerator, so limits is positive or negative infinite.

First shortcut rule :

3 is highest power of in numerator and 2 is highest power of in denominator.

Second shortcut rule :

2 is highest power of in numerator and 3 is highest power of in denominator.

Third shortcut rule :

If power of in numerator ang denominator is same such as equation in above, we can it soluted only with see the coefficient.

Example :

Solution from is 3.

Video III

The figure above shows the graph of if the function , is defined by , what is the value of ?

Answer :

Then, we change with 2.

So, the value of

Let the function be defined by , if . What is the value of ?

Answer :

, what is when ?

Fisrt, we must value of . With ways such as in below :

Second, we change in the equation become .

Third, we insert to where

Fourth, insert and to equation

So, the value of = 78 and 120

In the coordinate plane, the graph of intersect line at and What is the greatest possible value of the slope of ?

Answer :

Greatest =

Line =

is a slope.

Video IV

Function is VLT

Function is HLT = invertible.

Example 1 :

How many value of

The first we moved equation become

Then

From sterp 1, we can find

1. Value of is

2. Value of is

So,

Example 2

From equation in above we multiply right internode and left internode so, the equation become

is asymtot

We move equation in variable become equation in variable so the equation become :